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Dissertations / Theses on the topic 'Lattice gauge theories'
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1
Lowe, A. P. "Lattice gauge-Higgs theories." Thesis, University of Southampton, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378268.
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La, Cock Pierre. "Introduction to lattice gauge theories." Master's thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/17085.
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Includes bibliographical references.<br>The thesis is organized as follows. Part I is a general introduction to LGT. The theory is discussed from first principles, so that for the interested reader no previous knowledge is required, although it is assumed that he/she will be familiar with the rudiments of relativistic quantum mechanics. Part II is a review of QCD on the lattice at finite temperature and density. Monte Carlo results and analytical methods are discussed. An attempt has been made to include most relevant data up to the end of 1987, and to update some earlier reviews existing on the subject. To facilitate an understanding of the techniques used in LGT, provision has been made in the form of a separate Chapter on Group Theory and Integration, as well as four Appendices, one of which deals with Grassmann variables and integration.
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Coyle, P. K. "Accelerated techniques in lattice gauge theories." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636313.
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Lattice gauge theories, through Monte-Carlo simulations, provide the most powerful methods available for the non-perturbative study of many models. These techniques, however, become very inefficient as we approach the continuum limit, a problem known as Critical Slowing Down. Over recent years cluster methods have generated significant improvements over established techniques. In part I of this thesis we introduce such an algorithm for the <I>Z</I><SUB>2</SUB> Kalb-Ramond model in four dimensions, and find that we can improve the efficiency of the simulation by orders of magnitude. In the second part of this thesis we make preliminary investigations towards using duality transformations as an aid to improving numerical simulations, (where by duality we mean an extension of the technique of Kramers and Wannier). We study the compact <I>U</I>(1) lattice gauge theory in (2+1) dimensions as an example. The dual to this model is known to be a discrete Gaussian Solid On Solid model. We find the discrete nature of the model makes each update faster. However the structures which develop at high temperature, make naive simulations, overall, inefficient.
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Coddington, P. D. "Deconfinement transitions in lattice gauge theories]." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381129.
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Pickavance, Jennifer Linda. "Properties of mesons from lattice gauge theories." Thesis, University of Liverpool, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442758.
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Patella, Agostino. "Orientifold Planar Equivalence in Lattice Gauge Theories." Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85864.
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Baillie, Clive Fraser. "Lattice gauge theories : dynamical fermions and parallel computation." Thesis, University of Edinburgh, 1986. http://hdl.handle.net/1842/10701.
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Benassi, Costanza. "Su(3) lattice gauge theories and spin chains." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7171/.
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I modelli su reticolo con simmetrie SU(n) sono attualmente oggetto di studio sia dal punto di vista sperimentale, sia dal punto di vista teorico; particolare impulso alla ricerca in questo campo è stato dato dai recenti sviluppi in campo sperimentale per quanto riguarda la tecnica dell’intrappolamento di atomi ultrafreddi in un reticolo ottico. In questa tesi viene studiata, sia con tecniche analitiche sia con simulazioni numeriche, la generalizzazione del modello di Heisenberg su reticolo monodimensionale a simmetria SU(3). In particolare, viene proposto un mapping tra il modello di Heisenberg SU(3) e l’Hamiltoniana con simmetria SU(2) bilineare-biquadratica con spin 1. Vengono inoltre presentati nuovi risultati numerici ottenuti con l’algoritmo DMRG che confermano le previsioni teoriche in letteratura sul modello in esame. Infine è proposto un approccio per la formulazione della funzione di partizione dell’Hamiltoniana bilineare-biquadratica a spin-1 servendosi degli stati coerenti per SU(3).
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Stephenson, David Brian. "Non-perturbative field theories." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/13009.
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de, Flôor e. Silva Diego. "Critical behavior of multiflavor gauge theories." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6573.
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It is expected that the number of flavors in a gauge theory plays an important role in model building for physics beyond the standard model. We study the phase structure of the 12 flavor case through lattice simulations using a Rational Hybrid Monte Carlo (RHMC) algorithm for different masses, betas, and volumes, to investigate the question of conformality for this number of flavors. In particular, we analyze the Fisher's zeroes, in the vicinity of the endpoint of a line of first order phase transitions. This is motivated by previous studies that show how the complex renormalization group (RG) flows can be understood by looking at the zeros. The pinching of the imaginary part of these zeros with respect to increasing volume provides information about a possible unconventional continuum limit.
We also study the mass spectrum of a multiflavor linear sigma model with a splitting of fermion masses. The single mass linear sigma model successfully described a light sigma in accordance to recent lattice results. The extension to two masses predicts an unusual ordering of scalar masses, providing incentive for further lattice simulations with split quark mass.
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Lumia, Luca. "Digital quantum simulations of Yang-Mills lattice gauge theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/22355/.
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I metodi di calcolo tradizionali per le teorie di gauge su reticolo risultano problematici in regioni di diagrammi di fase a grandi valori del potenziale chimico o quando sono utilizzate per riprodurre la dinamica in tempo reale di un modello. Tali problemi possono essere evitati da simulazioni quantistiche delle teorie di gauge su reticolo, le quali stanno diventando sempre più riproducibili sperimentalmente, grazie ai recenti progressi tecnologici. In questa tesi formuliamo una versione delle teorie di Yang-Mills su reticolo appropriata per risolvere il problema della dimensione infinita dello spazio di Hilbert associato ai bosoni di gauge. Questa formulazione è adatta per essere riprodotta in un simulatore quantistico e ne implementiamo una completa simulazione su un computer quantistico digitale, sfruttando il framework Qiskit. In questa simulazione misuriamo le energie del ground state e i valori di aspettazione di alcuni Wilson loop al variare dell'accoppiamento della teoria, per studiarne le fasi e valutare la prestazione dei metodi usati.
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Lambrou, Eliana. "Phase structure of five-dimensional anisotropic lattice gauge theories." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/19579.
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The idea that we live in a higher-dimensional space was first introduced almost 100 years ago. In the past two decades many extra-dimensional models have been proposed in order to solve fundamental problems of nature such as the hierarchy problem. Most of them need exploration via non-perturbative approaches and Lattice Gauge Theory provides a tool for doing this. In this thesis, we make attempts to find a non-perturbative way to localize gauge fields that arise from five-dimensional SU(2) gauge theories on 3-branes. In 1984, it was proposed that the phase diagram of anisotropic extra-dimensional lattice gauge theories inherits a new phase, called the "layered" phase, where the gauge fields behave as four-dimensional ones. This was shown for the abelian case, but the existence of this new phase for the simplest non-abelian group, SU(2), was still in doubt. We investigated this system in large volumes using Monte Carlo simulations and we could not find a second order phase transition from a five-dimensional to a continuous four-dimensional theory when all directions were kept large. This made the model unattractive for further exploration as nothing suggests that a non-trivial fixed point could exist. The above investigation was done in a flat background metric. We extended the previous work by putting our theory into a slice of AdS5 space, usually called the warped background. The motivation for this is that our SU(2) theory looks like the gauge-sector of the Randall-Sundrum model, which does not have a concrete solution to the problem of localization of the gauge fields on a 3-brane. We carried out our investigation using the Mean-Field Approach and we present novel results for the phase diagram and measurements of important observables. In our implementation we have a finite extent of the extra dimension and one layer (or 3-brane) on each extra-dimensional coordinate. At weak coupling, we observed that each layer decouples one at a time in the transition to the fully layered phase of the system, forming a mixed phase, whereas there is a strong and sharp transition between the fully layered and the strong-coupling phase. Within the mixed phase, close to the transition into the layered phase, we found evidence that the system is four-dimensional acquiring a Yukawa mass and resembling a Higgs-like phase. The mixed phase grows as the curvature increases suggesting that for an infinite extra dimension the entire weak-coupling phase is mixed.
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Takimi, Tomohisa. "A non-perturbative study of supersymmetric lattice gauge theories." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/136759.
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Gelzer, Zechariah John. "Lattice gauge theories within and beyond the Standard Model." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5757.
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The Standard Model of particle physics has been very successful in describing fundamental interactions up to the highest energies currently probed in particle accelerator experiments. However, the Standard Model is incomplete and currently exhibits tension with experimental data for interactions involving $B$~mesons. Consequently, $B$-meson physics is of great interest to both experimentalists and theorists. Experimentalists worldwide are studying the decay and mixing processes of $B$~mesons in particle accelerators. Theorists are working to understand the data by employing lattice gauge theories within and beyond the Standard Model. This work addresses the theoretical effort and is divided into two main parts.
In the first part, I present a lattice-QCD calculation of form factors for exclusive semileptonic decays of $B$~mesons that are mediated by both charged currents ($B \to \pi \ell \nu$, $B_s \to K \ell \nu$) and neutral currents ($B \to \pi \ell^+ \ell^-$, $B \to K \ell^+ \ell^-$). The results are important for constraining or revealing physics beyond the Standard Model. This work uses MILC's $(2+1+1)$-flavor ensembles, with the HISQ action for the up, down, strange, and charm sea and valence quarks, and the clover action in the Fermilab interpretation for the $b$~quark. Simulations are carried out on five ensembles at three lattice spacings down to $\approx 0.088$~fm, with both physical and unphysical sea-quark masses. I present results for correlation-function fits and describe the chiral-continuum extrapolation and $z$~expansion of the form factors.
In the second part, I present the status of an ongoing lattice calculation of $SU(3)$ gauge theory with eight and $12$ fundamental fermions, in which I search for the endpoint of the line of first-order phase transitions in the mass--coupling plane. The results are important for understanding the phase diagram of these models, with possible applications to physics beyond the Standard Model. This work uses the staggered action and the nHYP-improved staggered action for the fermions, as well as the Wilson action in the fundamental and fundamental--adjoint representations for the gauge bosons. With the unimproved actions, I present results for a small lattice and describe the ongoing effort on larger lattices. I also discuss the shift symmetry on lattices with and without improved actions.
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Magnifico, Giuseppe <1991>. "Quantum simulation and topological phases in Lattice Gauge Theories." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amsdottorato.unibo.it/9254/1/tesi.pdf.
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Simulating quantum-mechanical systems is a very challenging issue due to the high computational costs. The main reason for this is related to the dimension of the Hilbert space that grows exponentially with the number of degrees of freedom, making an exact implementation impossible even for the most powerful today’s supercomputers.
On this ground it appears clear the need of a new simulation method, i.e. quantum simulation. The general idea is very simple: using a controllable quantum system, called quantum simulator, to emulate and to analyze another quantum system that usually results less controllable or accessible. Quantum simulation is currently a growing and multidisciplinary physical area that involves theoretical and experimental research. From the theoretical side, the main focus is on the study of simulation-models that create a mapping between the target physics and the simulator.
In the first two parts of this thesis, we explore these ideas by studying the ground-state properties and the real-time dynamics of a class of Zn lattice gauge theories in 1+1 dimensions, in which the gauge fields are coupled to fermionic matter. These models can be considered as quantum simulation-models of lattice 1+1 Quantum Electrodynamics (QED), which is the simplest gauge theory that shows non-trivial phenomena, like confinement, that are also observed in more complicated gauge theories, such as 3+1 Quantum Chromodynamics (QCD).
In the third part of this thesis, we unveil an interesting interplay of symmetry and topology by demonstrating the existence of symmetry-protected topological (SPT) phases in the presence of gauge interactions. More specifically, we introduce an alternative discretization of the Schwinger model leading to a new type of topological-QED. We use bosonization and Density-Matrix Renormalization Group (DMRG) techniques to analyze the phase diagram of the model, opening an interesting route to study topological phases of matter in the context of gauge theories.
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Bilson-Thompson, Sundance Osland. "Investigation of topology, instantons, and the Nahm transform in lattice QCD using highly improved operators." Title page, contents and abstract only, 2002. http://web4.library.adelaide.edu.au/theses/09PH/09phb5996.pdf.
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Kieu, T. D. "Theory and applications of lattice fermionic regularisations." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/10991.
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Vairinhos, Hélvio. "Large-N reduced models of SU(N) lattice guage theories." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670101.
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Bonnet, Frédéric D. R. "Improved actions in lattice QCD /." Title page, contents and introduction only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phb717.pdf.
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Maroncelli, Andrea. "QED and Abelian lattice gauge theories in 2+1 dimensions." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18042/.
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La simulazione di sistemi quantistici con molti gradi di libertà è oggi una sfida impegnativa per la comunità scientifica a causa degli elevati tempi computazionali che crescono esponenzialmente all'aumentare del numero di particelle.
Al seguito degli orizzonti aperti dall'articolo "Simulating physics with computers" di Feynman, oggi sono stati fatti numerosi progressi. Egli teorizzò un simulatore quantistico che fosse un vero e proprio apparato fisico che evolvesse nello stesso modo del sistema da studiare e la cui dinamica potesse essere controllata. Sulla base di quest'idea, oggi è possibile abbattere l'elevato costo computazionale che, in tal modo, cresce linearmente con la taglia dello spazio di Hilbert. Negli ultimi anni, infatti, sono stati svolti diversi esperimenti in numerosi laboratori. Ad esempio, sono stati utilizzati atomi ultrafreddi intrappolati in reticoli ottici per simulare fenomeni quantistici come la superconduttività.
Seguendo tale principio, in questo lavoro di tesi abbiamo implementato teorie abeliane, in special modo la QED, su reticolo bidimensionale che serviranno per una futura simulazione quantistica. Da qui, abbiamo analizzato alcuni fenomeni di attivo interesse di ricerca, come lo studio di transizioni di fase in modelli con simmetria $\mathbb{Z}_2$ e $\mathbb{Z}_3$, che presentano una fase confinata e una deconfinata, classificato gli stati gauge invarianti ed esaminato il meccanismo dello string-breaking su reticolo.
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Yoneyama, Kyoko [Verfasser]. "The Lattice Approach to Five Dimensional Gauge Theories / Kyoko Yoneyama." Wuppertal : Universitätsbibliothek Wuppertal, 2014. http://d-nb.info/1050188101/34.
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Mariani, Alessandro. "Finite-group Yang-Mills lattice gauge theories in the Hamiltonian formalism." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21183/.
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Nuovi sviluppi nel campo nelle tecniche sperimentali potrebbero presto permettere la realizzazione di simulatori quantistici, ovvero di sistemi quantomeccanici realizzabili sperimentalmente che descrivano una specifica Hamiltoniana di nostra scelta. Una volta costruito il sistema, si possono effettuare esperimenti per studiare il comportamento della teoria descritta dall'Hamiltoniana scelta. Un'interessante applicazione riguarda le teorie di gauge non-Abeliane come la Cromodinamica Quantistica, per le quali si hanno un certo numero di problemi irrisolti, in particolare nella regione a potenziale chimico finito. La principale sfida teorica per la realizzazione di un simulatore quantistico è quella di rendere lo spazio di Hilbert della teoria di gauge finito-dimensionale. Infatti in un esperimento si possono controllare realisticamente solo alcuni gradi di libertà del sistema quantistico, e certamente solo un numero finito. Seguendo alcune linee già tracciate in letteratura, nel presente lavoro ottieniamo uno spazio di Hilbert finito-dimensionale sostituendo il gruppo di gauge - un gruppo di Lie - con un gruppo finito, ad esempio uno dei suoi sottogruppi. Dopo una rassegna della teoria di Yang-Mills nel continuo e su reticolo, ne diamo la formulazione Hamiltoniana enfatizzando l'introduzione del potenziale chimico. A seguire, introduciamo le teorie basate su un qualsiasi gruppo di gauge finito, e proponiamo una soluzione ad un problema irrisolto di tali teorie, cioè la determinazione degli autovalori della densità di energia elettrica. Effettuiamo inoltre alcuni calcoli analitici della tensione di stringa in teorie con gruppo di gauge finito, e risolveremo esattamente alcune di esse in un caso semplificato. A finire, studieremo il comportamento dello stato fondamentale di tali teorie tramite un metodo variazionale, e offriremo alcune considerazioni conclusive.
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Peardon, Michael James. "A study of improved Monte-Carlo methods for lattice gauge theories." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/15616.
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This thesis is concerned with the study and improvement of methods for generating Monte-Carlo configurations used for providing non-perturbative numerical results from lattice gauge theories such as QCD, the theory of strong interactions between quarks and gluons. At present, lattice calculations require large amounts of CPU time on the largest supercomputers. In spite of this numerical assault, the majority of results generated still contain systematic errors from the use of the quenched approximation. In this approximation, employed to dramatically reduce computational costs, the effects of quantum fluctuations in the vacuum of fermion fields are ignored. Chapter 2 investigates the efficiency of a new approximate technique for dynamical fermion simulations which replaces the fermion action with the action of a large number of flavours of locally interacting auxiliary boson fields. The technique is shown to have problematic behaviour in the approach to the limit in which it exactly reproduces the required lattice gauge theory. The autocorrelation time, a measure of efficiency is shown to rise linearly in the number of boson fields employed. Chapter 3 proposes an improvement to this developing method which removes the bias of the approximation introduced. This avoids the computationally difficult approach to the exact limit of the approximation. Chapter 4 involves the calculation of the mass of the scalar glueball of QCD using large lattice spacings to avoid the high penalty for the approach to the continuum limit with an "improved" lattice action to remove the significant discretisation artifacts present at these spacings.
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Lau, Richard. "SO(N) gauge theories in 2+1 dimensions." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:fa9dae0a-70c2-467a-8aa7-daff5531ff10.
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We calculate the string tensions, mass spectrum, and deconfining temperatures of <i>SO(N</i>) gauge theories in 2+1 dimensions. After a review of lattice field theory, we describe how we simulate the corresponding lattice gauge theories, construct operators to project on to specific states, and extrapolate values to the continuum limit. We discuss how to avoid possible complications such as finite size corrections and the bulk transition. <i>SO(N</i>) gauge theories have become recently topical since they do not have a fermion sign problem, are orbifold equivalent to <i>SU(N</i>) gauge theories, and share a common large-<i>N</i> limit in their common sector of states with <i>SU(N</i>) gauge theories. This motivates us to compare the physical properties of <i>SO(N</i>) and <i>SU(N</i>) gauge theories between 'group equivalences', which includes Lie algebra equivalences such as <i>SO</i>(6) and <i>SU</i>(4), and particularly a large-<i>N</i> equivalence. We discuss the large-<i>N</i> orbifold equivalence between <i>SO(N</i>) and <i>SU(N</i>) gauge theories, which relates the large-<i>N</i> gauge theories perturbatively. Using large-<i>N</i> extrapolations at fixed 't Hooft coupling, we test to see if <i>SO(N</i>) gauge theories and <i>SU(N</i>) gauge theories share non-perturbative properties at the large-<i>N</i> limit. If these group equivalences lead to similar physics in the gauge theories, then we could imagine doing finite chemical potential calculations that are currently intractable in <i>SU(N</i>) gauge theories by calculating equivalent quantities in the corresponding <i>SO(N</i>) gauge theories. We show that the <i>SO(N</i>) and <i>SU(N</i>) values match between group equivalences and at the large-<i>N</i> limit.
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Liu, Yuzhi. "Renormalization group and phase transitions in spin, gauge, and QCD like theories." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4872.
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In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).
We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete β functions. The motivation of calculating the discrete β functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain.
We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation.
We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare the distribution of Fisher zeros for lattice gauge models with four and twelve light fermion flavors. We also briefly discuss the scaling of the zeros and its connection with the infrared fixed point (IRFP) and the mass anomalous dimension.
Conventional numerical simulations suffer from the critical slowing down at the critical region, which prevents one from simulating large system. In order to reach the continuum limit in the lattice gauge theories, one needs either large volume or clever extrapolations. TRG is a new computational method that may calculate exponentially large system and works well even at the critical region. We formulate the TRG blocking procedure for the two dimensional O(2) (or XY ) and O(3) spin models and discuss possible applications and generalizations of the method to other spin and lattice gauge models.
We start the thesis with the introduction and historical background of the RG in general.
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Marchese, Luca. "Quantum simulation of abelian and non-abelian gauge theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24857/.
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Le teorie di gauge sono onnipresenti nella fisica moderna, trovando applicazioni in diversi ambiti, dal modello standard alla fisica della materia condensata. Il recente sviluppo della tecnologia quantistica apre ora le porte a nuove tecniche utili al loro approfondimento, ampliando la nostra conoscenza di questi modelli ed oltrepassando i limiti degli approcci basati sul metodo di Montecarlo, quali il problema del segno e l'impossibilità di studiare la dinamica dei sistemi in tempo reale.
Questa tesi si concentra sull'implementazione di una simulazione per una teoria di Yang-Mills su reticolo con un gruppo di simmetria finito. Abbiamo testato diversi gruppi, sia abeliani (Z2 e Z4) che non abeliani (D4), per i quali abbiamo emulato i risultati di un computer quantistico in un modello a 2+1 dimensioni. Una caratteristica fondamentale di questi modelli è la presenza di vincoli sullo spazio di Hilbert che determinano quali stati possono entrare nella dinamica. Nel caso abeliano siamo in grado di sfruttare la minore dimensione dello spazio degli stati fisici per introdurre una codifica più efficiente nella base computazionale. Nel caso invece di una simmetria data da gruppi non abeliani, questo metodo non può essere direttamente implementato a causa della comparsa di stati più complessi. Usando la misura del valore di aspettazione di vari Wilson loop, abbiamo trovato che tutti i sistemi analizzati presentano due fasi, una confinata e una non confinata. Sfruttando la semplicità dei sistemi abeliani siamo anche riusciti in quei casi a verificare direttamente la legge del perimetro e la legge dell'area, che descrivono il comportamento dei Wilson loop nelle due differenti fasi.
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Pickup, Thomas. "Investigating the conformal window of SU(N) gauge theories." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:79a22d60-86b2-4e53-abd6-50edbc979e42.
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In this thesis we are concerned with the existence of infrared fixed points and the conformal window for gauge theories with fermions. We are particularly interested in those theories that are candidates for walking technicolor. We discuss the background of technicolor and the techniques relevant to a theoretical understanding of the conformal window. Following this we extend the ideas of metric confinement and causal analyticity to theories with fermions in non-fundamental representations. We use these techniques to, respectively, provide a lower bound on the lower end of the conformal window and to provide a measure of perturbativity. As well as analytic calculations we use lattice techniques to investigate two particular candidate theories for walking technicolor - SU(2) with two adjoint fermions and with six fundamental fermions. We use Schrodinger Functional techniques to investigate the running of the theory across a wide range of scales. We measure both the running of the coupling and an estimator for the fermion mass anomalous dimension, $gamma$. We find that both theories are consistent with an infrared fixed-point. However, paying particular attention to our error estimates, we are unable to absolutely confirm their existence. This is a not unexpected result for SU(2) with two adjoint fermions but is rather surprising for SU(2) with only six fundamental fermions. In the region where we are consistent with a fixed point we find $0.05<gamma<0.56$ for $SU(2)$ with two adjoint fermions and $0.135<gamma<1.03$ for $SU(2)$ with six fundamental fermions. The measurement of $gamma$ for $SU(2)$ with two adjoint fermions is the first determination of $gamma$ for any candidate theory of walking technicolor.
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Vogt, Hannes Andreas [Verfasser], and Hugo [Akademischer Betreuer] Reinhardt. "Strongly Coupled Theories in Lattice Coulomb Gauge / Hannes Andreas Vogt ; Betreuer: Hugo Reinhardt." Tübingen : Universitätsbibliothek Tübingen, 2017. http://d-nb.info/1167247256/34.
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Vogt, Hannes [Verfasser], and Hugo [Akademischer Betreuer] Reinhardt. "Strongly Coupled Theories in Lattice Coulomb Gauge / Hannes Andreas Vogt ; Betreuer: Hugo Reinhardt." Tübingen : Universitätsbibliothek Tübingen, 2017. http://d-nb.info/1167247256/34.
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Arnault, Pablo. "Discrete-time quantum walks and gauge theories." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066135/document.
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Un ordinateur quantique (OQ), i.e. utilisant les ressources de la physique Q, superposition et intrication, pourrait fournir un gain exponentiel de temps de calcul. Une simulation utilisant ces ressources est appelée simulation Q (SQ). L’avantage des SQs sur les simulations classiques est bien établi au niveau théorique, i.e. software. Leur avantage pratique requiert un hardware Q. L’OQ, sous-entendu universel (cf. plus bas), n’a pas encore vu le jour, mais les efforts en ce sens sont croissants et variés. Aussi la SQ a-t-elle déjà été illustrée par de nombreuses expériences de principe, grâce à des calculateurs ou simulateurs Qs de taille réduite. Les marches Qs (MQs) sont des schémas de SQ particulièrement étudiés, étant des briques élémentaires pour concevoir n’importe quel algorithme Q, i.e. pour le calcul Q universel. La présente thèse est un pas de plus vers une simulation des théories Qs des champs basée sur les MQs à temps discret (MQTD). En effet, il est montré, dans certains cas, comment les MQTD peuvent simuler, au continu, l'action d'un champ de jauge Yang-Mills sur de la matière fermionique, et la rétroaction de cette-dernière sur la dynamique du champ de jauge. Les schémas proposés préservent l’invariance de jauge au niveau de la grille d’espace-temps, i.e. pas seulement au continu. Il est proposé (i) des équations de Maxwell sur grille, compatibles avec la conservation du courant sur la grille, et (ii) une courbure non-abélienne définie sur la grille. De plus, il est montré comment cette matière fermionique à base de MQTD peut être couplée à des champs gravitationnels relativistes du continu, i.e. des espaces-temps courbes, en dimension 1+2<br>A quantum (Q) computer (QC), i.e. utilizing the resources of Q physics, superposition of states and entanglement, could fournish an exponential gain in computing time. A simulation using such resources is called a Q simulation (QS). The advantage of QSs over classical ones is well established at the theoretical, i.e. software level. Their practical benefit requires their implementation on a Q hardware. The QC, i.e. the universal one (see below), has not seen the light of day yet, but the efforts in this direction are both growing and diverse. Also, QS has already been illustrated by numerous experimental proofs of principle, thanks too small-size and specific-task Q computers or simulators. Q walks (QWs) are particularly-studied QS schemes, being elementary bricks to conceive any Q algorithm, i.e. to achieve so-called universal Q computation. The present thesis is a step more towards a simulation of Q field theories based on discrete-time QWs (DTQWs). Indeed, it is shown, in certain cases, how DTQWs can simulate, in the continuum, the action of Yang-Mills gauge fields on fermionic matter, and the retroaction of the latter on the gauge-field dynamics. The suggested schemes preserve gauge invariance on the spacetime lattice, i.e. not only in the continuum. In the (1+2)D Abelian case, consistent lattice equivalents to both Maxwell’s equations and the current conservation are suggested. In the (1+1)D non-Abelian case, a lattice version of the non-Abelian field strength is suggested. Moreover, it is shown how this fermionic matter based on DTQWs can be coupled to relativistic gravitational fields of the continuum, i.e. to curved spacetimes, in several spatial dimensions
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Bibireata, Daniel. "Super Yang-Mills theories on the lattice." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1117586284.
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Thesis (Ph. D.)--Ohio State University, 2005.<br>Title from first page of PDF file. Document formatted into pages; contains x, 94 p.; also includes graphics Includes bibliographical references (p. 52-54). Available online via OhioLINK's ETD Center
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Schweizer, Christian [Verfasser], та Immanuel [Akademischer Betreuer] Bloch. "Minimal instances for ℤ₂ lattice gauge theories and spin pumps / Christian Schweizer ; Betreuer: Immanuel Bloch". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2019. http://d-nb.info/1196529140/34.
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García, Vera Miguel Francisco. "Investigating the large N limit of SU(N) Yang-Mills gauge theories on the lattice." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18123.
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In dieser Arbeit praesentieren wir Resultate der topologischen Suszeptibilitaet “chi” und untersuchen die Faktorisierung der reinen SU(N) Yang-Mills Eichtheorie im 't Hooft'schen Grenzwert grosser N. Ein entscheidender Teil der Berechnung von chi in der Gittereichtheorie ist die Abschaetzung des topologischen Ladungsdichtekorrelators, die durch ein schlechtes Signal-Rausch- Verhaeltnis beeintraechtigt ist. Um dieses Problem abzuschwaechen, fuehren wir einen neuen, auf einem mehrstufigen Vorgehen beruhenden Algorithmus ein, um die Korrelationsfunktion von Observablen zu berechnen, die mit dem Yang-Mills Gradientenfluss geglaettet wurden. Angewandt auf unsere Observablen, erhalten wir Ergebnisse, deren Fehlerskalierung besser ist, als die von herkoemmlichen Monte-Carlo Simulationen.
Wir bestimmen die topologische Suszeptibilitaet in der reinen Yang-Mills Eichtheorie fuer Eichgruppen mit N = 4,5,6 und drei verschiedenen Gitterabstaenden. Um das Einfrieren der Topologie zu umgehen, wenden wir offene Randbedingungen an. Zusaetzlich wenden wir die korrekte Definition der topologischen Ladungsdichte durch den Gradientenfluss an. Unser Endresultat im des Grenzfalls von grossen N repraesentiert eine neue Qualitaet in der Verifikation der Witten-Veneziano Formel.
Schliesslich benutzen wir die Gitterformulierung, um die Erwartungswertfaktorisierung des Produkts eichinvarianter Operatoren im Grenzwert grosser N zu verifizieren. Wir arbeiten mit durch den Yang-Mills Grandientenfluss geglaetteten Wilsonschleifen und Simulationen bis zur Eichgruppe SU(8). Die Extrapolationen zu grossen N sind in Ueberstimmung mit der Faktorisierung sowohl fuer endlichen Gitterabstand als auch in Kontinnumslimes. Unsere Daten erlauben uns nicht nur die Verifizierung der Faktorisierung, sondern auch einen hochpraezisen Test des 1/N Skalierungsverhaltens. Hier konnten wir das quadratische Skalierungsverhalten in 1/N finden, welches von 't Hooft vorhergesagt wurde.<br>In this thesis we present results for the topological susceptibility “chi”, and investigate the property of factorization in the 't Hooft large N limit of SU(N) pure Yang-Mills gauge theory. A key component in the lattice gauge theory computation of chi is the estimation of the topological charge density correlator, which is affected by a severe signal to noise problem. To alleviate this problem, we introduce a novel algorithm that uses a multilevel type approach to compute the correlation function of observables smoothed with the Yang-Mills gradient flow. When applied to our observables, the results show an scaling of the error which is better than the one of standard Monte-Carlo simulations.
We compute the topological susceptibility in the pure Yang-Mills gauge theory for the gauge groups with N = 4, 5, 6 and three different lattice spacings. In order to deal with the freezing of topology, we use open boundary conditions. In addition, we employ the theoretically sound definition of the topological charge density through the gradient flow. Our final result in the limit N to infinity, represents a new quality in the verification of the Witten-Veneziano formula.
Lastly, we use the lattice formulation to verify the factorization of the expectation value of the product of gauge invariant operators in the large N limit. We work with Wilson loops smoothed with the Yang-Mills gradient flow and simulations up to the gauge group SU(8). The large N extrapolations at finite lattice spacing and in the continuum are compatible with factorization. Our data allow us not only to verify factorization, but also to test the 1/N scaling up to very high precision, where we find it to agree very well with a quadratic series in 1/N as predicted originally by 't Hooft for the case of the pure Yang-Mills gauge theory.
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Arndt, Daniel. "Chiral perturbation theory on the lattice and its applications /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/9693.
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Hammant, Thomas Christopher. "Perturbative calculations in lattice gauge theories and the application of statistical mechanics to soft condensed matter systems." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608097.
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Edwards, Samuel Ryan Verfasser], Lorenz von [Akademischer Betreuer] Smekal, and Jochen [Akademischer Betreuer] [Wambach. "Topology, symmetry, and phase transitions in lattice gauge theories / Samuel Ryan Edwards. Betreuer: Lorenz von Smekal ; Jochen Wambach." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2013. http://d-nb.info/110645460X/34.
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Edwards, Samuel Ryan [Verfasser], Lorenz von Akademischer Betreuer] Smekal, and Jochen [Akademischer Betreuer] [Wambach. "Topology, symmetry, and phase transitions in lattice gauge theories / Samuel Ryan Edwards. Betreuer: Lorenz von Smekal ; Jochen Wambach." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2013. http://nbn-resolving.de/urn:nbn:de:tuda-tuprints-34133.
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Olivares, Legal Fabian Andres [Verfasser], and Markus K. [Akademischer Betreuer] Oberthaler. "Towards Lattice Gauge Theories in Ultracold Mixtures of Sodium and Lithium / Fabián Andrés Olivares Legal ; Betreuer: Markus K. Oberthaler." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177149362/34.
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Wellegehausen, Björn-Hendrik [Verfasser], Andreas [Akademischer Betreuer] Wipf, Uwe-Jens [Akademischer Betreuer] Wiese, and Simon [Akademischer Betreuer] Hands. "Phase diagrams of exceptional and supersymmetric lattice gauge theories / Björn-Hendrik Wellegehausen. Gutachter: Andreas Wipf ; Uwe-Jens Wiese ; Simon Hands." Jena : Thüringer Universitäts- und Landesbibliothek Jena, 2012. http://d-nb.info/1027706843/34.
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Scherzer, Manuel [Verfasser], and Ion-Olimpiu [Akademischer Betreuer] Stamatescu. "Phase transitions in lattice gauge theories: From the numerical sign problem to machine learning / Manuel Scherzer ; Betreuer: Ion-Olimpiu Stamatescu." Heidelberg : Universitätsbibliothek Heidelberg, 2019. http://d-nb.info/1191760340/34.
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Wellegehausen, Björn-Hendrik [Verfasser], Andreas Akademischer Betreuer] Wipf, Uwe-Jens [Akademischer Betreuer] [Wiese, and Simon [Akademischer Betreuer] Hands. "Phase diagrams of exceptional and supersymmetric lattice gauge theories / Björn-Hendrik Wellegehausen. Gutachter: Andreas Wipf ; Uwe-Jens Wiese ; Simon Hands." Jena : Thüringer Universitäts- und Landesbibliothek Jena, 2012. http://d-nb.info/1027706843/34.
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Ferreira, Miguel Jorge Bernabé. "Teorias de campos discretas e modelos topológicos." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-03052012-082048/.
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Neste trabalho estudamos as teorias de gauge puras (sem campo de matéria) na rede em três dimensões. Em especial, estudamos a subclasse das teorias topológicas. A maneira como denimos e tratamos as teorias de gauge e diferente, mas equivalente, à forma usual apresentada em [2, 3]. Definimos estas teorias via o formalismo de Kuperberg, que é um formalismo puramente matemático de um invariante topológico de variedades tridimensionais. Este formalismo, embora bastante abstrato, pode ser adaptado para descrever as classes de modelos das teorias de gauge na rede, e traz várias vantagens, pois possibilita que tratemos de teorias topológicas e não topológicas, além da fácil identicação dos limites topológicos da função de partição. Estudamos também a classe das teorias chamadas quase topológicas, que podem ser pensadas como deformações de teorias topológicas. Em particular, consideramos teorias de gauge com grupo de gauge Z2, que é o grupo de gauge mais simples possível com dinâmica não trivial. Dentro das teorias de gauge, identicamos as classes de modelos que são quase topológicos, além de outras classes nas quais a função de partição pode ser trivialmente calculada. A função de partição foi calculada explicitamente no caso quase topológico em duas situações: sobre a esfera tridimensional S3 e sobre o toroS1x S1x S1x, que representa uma rede com condições periódicas de contorno. Dois modelos físicos de teorias de gauge, ainda com grupo de gauge Z2, foram estudados: o modelo com ação de Wilson SW = Pfaces [Tr(g) - 1] e o modelo com ação spin-gauge SSG = Pfaces Tr(g). No limite de baixa temperatura ambos os modelos mostram-se ser topológicos, enquanto que no limite de alta temperatura mostraram-se ser trivialmente calculáveis.<br>In this work we studied the class of models of pure lattice gauge theories (without matter elds) in three dimensions. Especially, we studied the subclass of topological theories. Lattice gauge theories were dened in an unusual way, unlike the description shown in [2, 3]. We dened lattice gauge theories via the Kuperberg\'s formalism [4], which is a mathematical model for a topological invariant of 3-manifolds. Such formalism, although completely abstract, can describe the class of models of lattice gauge theories because it can describe both topological and non topological theories, besides it provides an easy identication of the partition function topological limits. We also studied the class of theories called quasi topological, which can be thought as deformations of topological theories. As an example, we consider Z2 as gauge group, because it is the simplest group that does not imply trivial dynamics. Inside this class of models we identify the subclasses of quasi topological theories and also other classes in which the partition function can be trivially computed. The partition function was explicitly computed in two situations: on the 3-sphere S3 and on the 3-manifold S1 x S1 x S1 that represents periodic boundary conditions. Two physical models were studied: the model with Wilson\'s action SW(conf)1 and the model with spin-gauge action SSG(conf)2. In the low temperature limit both models shown to be topological and in the high temperature limit they could be trivially computed.
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Smiseth, Jo. "Criticality and novel quantum liquid phases in Ginzburg--Landau theories with compact and non-compact gauge fields." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Natural Sciences and Technology, 2005. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-583.
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<p>We have studied the critical properties of three-dimensional U(1)-symmetric lattice gauge theories. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. This thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication.</p><p>Paper I: Critical properties of the 2+1-dimensional compact abelian Higgs model with gauge charge q=2 are studied. We introduce a novel method of computing the third moment M<sub>3</sub> of the action which allows us to extract correlation length and specific heat critical exponents ν and α without invoking hyperscaling. Finite-size scaling analysis of M<sub>3</sub> yields the ratio (1+α)/ν and 1/ν separately. We find that α and ν vary along the critical line of the theory, which however exhibits a remarkable resilience of Z<sub>2</sub> criticality. We conclude that the model is a fixed-line theory, which we propose to characterize the zero temperature quantum phase transition from a Mott-Hubbard insulator to a charge fractionalized insulator in two spatial dimensions.</p><p>Paper II: Large scale Monte Carlo simulations are employed to study phase transitions in the three-dimensional compact abelian Higgs model in adjoint representations of the matter field, labeled by an integer q, for q=2,3,4,5. We also study various limiting cases of the model, such as the Z<sub>q</sub> lattice gauge theory, dual to the 3DZ<sub>q</sub> spin model, and the 3D xy spin model which is dual to the Z<sub>q</sub> lattice gauge theory in the limit q → ∞. In addition, for benchmark purposes, we study the 2D square lattice 8-vertex model, which is exactly solvable and features non-universal critical exponents. The critical exponents α and ν are calculated from finite size scaling of the third moment of the action, and the method is tested thoroughly on models with known values for these exponents. We have found that for q=3, the three-dimensional compact abelian Higgs model exhibits a second order phase transition line which joins a first order phase transition line at a tricritical point. The results for q=2 in Paper I are reported with a higher lever of detail.</p><p>Paper III: This paper is based on a talk by F. S. Nogueira in the Aachen HEP 2003 conference where a review of the results for the compact abelian Higgs model from Paper I and Paper II was presented, as well as the results for the q=1 case studied by F. S. Nogueira, H. Kleinert and A. Sudbø.</p><p>Paper IV: We study the effects of a Chern-Simons (CS) term in the phase structure of two different abelian gauge theories in three dimensions. By duality transformations we show how the compact U(1) gauge theory with a CS term for certain values of the CS coupling can be written as a gas of vortex loops interacting through steric repulsion. This theory is known to exhibit a phase transition governed by proliferation of vortex loops. We also employ Monte Carlo simulations to study the non-compact U(1) abelian Higgs model with a CS term. Finite size scaling of the third moment of the action yields critical exponents α and ν that vary continuously with the strength of the CS term, and a comparison with available analytical results is made.</p><p>Paper V: The critical properties of N-component Ginzburg-Landau theory are studied in d=2+1 dimensions. The model is dualized to a theory of N vortex fields interacting through a Coulomb and a screened potential. The model with N=2 shows two anomalies in the specific heat. From Monte Carlo simulations we calculate the critical exponents α and ν and the mass of the gauge field. We conclude that one anomaly corresponds to an inverted 3D xy fixed point, while the other corresponds to a 3D xy fixed point. There are N fixed points, namely one corresponding to an inverted 3D xy fixed point, and N-1corresponding to neutral 3D xy fixed points. Applications are briefly discussed.</p><p>Paper VI: The phase diagram and critical properties of the N-component London superconductor are studied both analytically and through large-scale Monte-Carlo simulations in d=2+1 dimensions. The model with different bare phase stiffnesses for each flavor is a model of superconductivity which should arise out of metallic phases of light atoms under extreme pressure. A projected mixture of electronic and protonic condensates in liquid metallic hydrogen under extreme pressure is the simplest example, corresponding to N=2 with individually conserved matter fields. We compute critical exponents α and ν for N=2 and N=3. The results from Paper V are presented at a higher level of detail. For the arbitrary N case, there are N fixed points,namely one charged inverted 3D xy fixed point, and N-1 neutral 3D xy fixed points. We explicitly identify one charged vortex mode and N-1 neutral vortex modes. The model for N=2 and equal bare phase stiffnesses corresponds to a field theoretical description of an easy-plane quantum antiferromagnet. In this case, the critical exponents are computed and found to be non 3D xy values. Furthermore, we study the model in an external magnetic field, and find a novel feature, namely N-1 superfluid phases arising out of N charged condensates. In particular, for N=2 we point out the possibility of two novel types of field-induced phase transitions in ordered quantum fluids: i) A phase transition from a superconductor to a superfluid or vice versa, driven by tuning an external magnetic field. This identifies the superconducting phase of liquid metallic hydrogen as a novel quantum fluid. ii) A phase transition corresponding to a quantum fluid analogue of sublattice melting, where a composite field-induced Abrikosov vortex lattice is decomposed and disorders the phases of the constituent condensate with lowest bare phase stiffness. Both transitions belong to the 3D xy universality class.</p><p>Paper VII: We consider the vortex superconductor with two individually conserved condensates in a finite magnetic field. The ground state is a lattice of cocentered vortices in both order parameters. We find two novel phase transitions when temperature is increased at fixed magnetic field. i) A "vortex sublattice melting" transition where vortices in the field with lowest phase stiffness ("light vortices") loose cocentricity with the vortices with large phase stiffness ("heavy vortices"), entering a liquid state (the structure factor of the light vortex sublattice vanishes continuously.) This transition is in the 3D xy universality class. ii) A first order melting transition of the lattice of heavy vortices in a liquid of light vortices.</p><p>Paper VIII: We report on large-scale Monte Carlo simulations of a novel type of a vortex matter phase transition which should take place in a three dimensional two-component superconductor. We identify the regime where first, at a certain temperature a field-induced lattice of co-centered vortices of both order parameters melts, causing the system to loose superconductivity. In this state the two-gap system retains a broken composite symmetry and we observe that at a higher temperature it undergoes an extra phase transition where the disordered composite one-flux-quantum vortex lines are "ionized" into a "plasma" of constituent fractional flux vortex lines in individual order parameters. This is the hallmark of the superconductor-to-superfluid-to-normal fluid phase transitions projected to occur in e.g. liquid metallic hydrogen.</p>
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Sommer, Rainer [Gutachter], Ulrich [Gutachter] Wolff, and Biagio [Gutachter] Lucini. "Investigating the large N limit of SU(N) Yang-Mills gauge theories on the lattice / Gutachter: Rainer Sommer, Ulrich Wolff, Biagio Lucini." Berlin : Humboldt-Universität zu Berlin, 2017. http://d-nb.info/1189328984/34.
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Volkholz, Jan. "Nonperturbative studies of quantum field theories on noncommutative spaces." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2007. http://dx.doi.org/10.18452/15712.
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Diese Arbeit befasst sich mit Quantenfeldtheorien auf nicht-kommutativen Räumen. Solche Modelle treten im Zusammenhang mit der Stringtheorie und mit der Quantengravitation auf. Ihre nicht-störungstheoretische Behandlung ist üblicherweise schwierig. Hier untersuchen wir jedoch drei nicht-kommutative Quantenfeldtheorien nicht-perturbativ, indem wir die Wirkungsfunktionale in eine äquivalente Matrixformulierung übersetzen. In der Matrixdarstellung kann die jeweilige Theorie dann numerisch behandelt werden. Als erstes betrachten wir ein regularisiertes skalares Modell auf der nicht-kommutativen Ebene und untersuchen den Kontinuumslimes bei festgehaltener Nicht-Kommutativität. Dies wird auch als Doppelskalierungslimes bezeichnet. Insbesondere untersuchen wir das Verhalten der gestreiften Phase. Wir finden keinerlei Hinweise auf die Existenz dieser Phase im Doppelskalierungslimes. Im Anschluss daran betrachten wir eine vier-dimensionale U(1) Eichtheorie. Hierbei sind zwei der räumlichen Richtungen nicht-kommutativ. Wir untersuchen sowohl die Phasenstruktur als auch den Doppelskalierungslimes. Es stellt sich heraus, dass neben den Phasen starker und schwacher Kopplung eine weitere Phase existiert, die gebrochene Phase. Dann bestätigen wir die Existenz eines endlichen Doppelskalierungslimes, und damit die Renormierbarkeit der Theorie. Weiterhin untersuchen wir die Dispersionsrelation des Photons. In der Phase mit schwacher Kopplung stimmen unsere Ergebnisse mit störungstheoretischen Berechnungen überein, die eine Infrarot-Instabilität vorhersagen. Andererseits finden wir in der gebrochenen Phase die Dispersionsrelation, die einem masselosen Teilchen entspricht. Als dritte Theorie betrachten wir ein einfaches, in seiner Kontinuumsform supersymmetrisches Modell, welches auf der "Fuzzy Sphere" formuliert wird. Hier wechselwirken neutrale skalare Bosonen mit Majorana-Fermionen. Wir untersuchen die Phasenstruktur dieses Modells, wobei wir drei unterschiedliche Phasen finden.<br>This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore a scalar model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized scalar model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations.
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Carrozza, Sylvain. "Tensorial methods and renormalization in Group Field Theories." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112147/document.
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Cette thèse présente une étude détaillée de la structure de théories appelées GFT ("Group Field Theory" en anglais),à travers le prisme de la renormalisation. Ce sont des théories des champs issues de divers travaux en gravité quantique, parmi lesquels la gravité quantique à boucles et les modèles de matrices ou de tenseurs. Elles sont interprétées comme desmodèles d'espaces-temps quantiques, dans le sens où elles génèrent des amplitudes de Feynman indexées par des triangulations,qui interpolent les états spatiaux de la gravité quantique à boucles. Afin d'établir ces modèles comme des théories deschamps rigoureusement définies, puis de comprendre leurs conséquences dans l'infrarouge, il est primordial de comprendre leur renormalisation. C'est à cette tâche que cette thèse s'attèle, grâce à des méthodes tensorielles développées récemment,et dans deux directions complémentaires. Premièrement, de nouveaux résultats sur l'expansion asymptotique (en le cut-off) des modèles colorés de Boulatov-Ooguri sont démontrés, donnant accès à un régime non-perturbatif dans lequel une infinité de degrés de liberté contribue. Secondement, un formalisme général pour la renormalisation des GFTs dites tensorielles (TGFTs) et avec invariance de jauge est mis au point. Parmi ces théories, une TGFT en trois dimensions et basée sur le groupe de jauge SU(2) se révèle être juste renormalisable, ce qui ouvre la voie à l'application de ce formalisme à la gravité quantique<br>In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory.Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one hand,and to matrix models and tensor models on the other hand. They model quantum space-time, in the sense that their Feynman amplitudes label triangulations, which can be understood as transition amplitudes between LQG spin network states. The question of renormalizability is crucial if one wants to establish interesting GFTs as well-defined (perturbative) quantum field theories, and in a second step connect them to known infrared gravitational physics. Relying on recently developed tensorial tools, this thesis explores the GFT formalism in two complementary directions. First, new results on the large cut-off expansion of the colored Boulatov-Ooguri models allow to explore further a non-perturbative regime in which infinitely many degrees of freedom contribute. The second set of results provide a new rigorous framework for the renormalization of so-called Tensorial GFTs (TGFTs) with gauge invariance condition. In particular, a non-trivial 3d TGFT with gauge group SU(2) is proven just-renormalizable at the perturbative level, hence opening the way to applications of the formalism to (3d Euclidean) quantum gravity
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Nishino, Kazuyoshi. "An Application of the Peter-Weyl Theorem to Non-Abelian Lattice Gauge Theory." 京都大学 (Kyoto University), 1993. http://hdl.handle.net/2433/168943.
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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである<br>Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第5306号<br>理博第1480号<br>新制||理||821(附属図書館)<br>UT51-93-F63<br>京都大学大学院理学研究科数理解折専攻<br>(主査)教授 中西 襄, 教授 柏原 正樹, 教授 荒木 不二洋<br>学位規則第4条第1項該当
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Necco, Silvia. "The static quark potential and scaling behavior of SU(3) lattice Yang-Mills theory." Doctoral thesis, [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=96870672X.
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Santos, Pedro Alexandre dos [UNESP]. "Estudo da quebra espontânea de simetria de calibre: mapas dinâmicos, ações complexas, teorias de campo em rede e (im)possibilidade." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/149898.
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Previous issue date: 2017-02-20<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Neste trabalho, fez-se uma introdução aos mapas dinâmicos, um conjunto de técnicas desenvolvido por Mat- sumoto, Umezawa, entre outros colaboradores, e a prescrição i na formulação usual da teoria quântica de campos no contı́nuo para descrever quebra espontânea de simetria de calibre (QES). Esta técnica baseia-se na utilização de representações unitárias não equivalentes, para construir as diferentes fases fı́sicas observadas em sistemas que apresenta QES. Introduzido o mapa dinâmico, tentou-se adaptar esta coleção de técnicas junto da prescrição i em rede, obtendo como resultado que a primeira não é satisfatoriamente desenvolvida em redes finitas, entretanto no limite termodinâmico o resultado aparenta estar adequado. Então, visitou-se o Teorema de Elitzur para as descrições obtidas por esta ferramenta, isto é, tentou-se demonstrar o Teorema de Elitzur para modelos com termos complexos provenientes da prescrição i . Uma vez que este não forneceu as informações esperadas, aplicou-se outras discussões para investigar a possibilidade da quebra espontânea de simetria de calibre em rede. Neste texto, o ferramental adotado se baseou em uma discussão apresentada por Splittorff.<br>In this work, an introduction to dynamic maps, a set of techniques developed by Matsumoto, Umezawa, among other collaborators, and the iepsilon prescription in the usual formulation of the quantum field theory in the continuum to describe spontaneous breaking of gauge symmetry (QES). This technique is based on the use of non-equivalent unitary representations to construct the different physical phases observed in systems that apresented QES. Introduced dynamic map, it was started the adaptation fo this collection of techniques to- gether with the prescription i in lattice, obtaining as a result that the first one is not satisfactorily developed in finite lattice, however in the thermodynamic limit the apparent result is adequate. Then the Elitzur’s The- orem was visited for the descriptions obtained by this tool, that is, it was attempted to demonstrate Elitzur’s Theorem for models with complex terms from the prescription i . As soon as the latter did not provide the expected information, other discussions were conducted to investigate the possibility of spontaneous breaking of lattice gauge symmetry. In this text, the tooling adopted was based on a discussion presented by Splittorff.
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Edwards, Samuel Ryan. "Topology, symmetry, and phase transitions in lattice gauge theories." Phd thesis, 2013. https://tuprints.ulb.tu-darmstadt.de/3413/1/edwardsPhD.pdf.
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We study connections between global symmetries, topological objects, and phase transitions in non-abelian gauge theories. The characterization of deconfinement as a spontaneous symmetry breaking transition in SU(N) gauge theories with static quarks, and its description in terms of Z_N interfaces, serve as our motivation. We study 2+1 dimensional SU(N) gauge theories with N<=4, which are candidates for the exploitation of universality with corresponding N-state Potts models. Exact results from the 2d spin systems are used to obtain critical couplings, transition temperatures, exponents, and the behavior of string tensions at criticality. Kramers-Wannier duality emerges between center vortices and electric fluxes at the phase transition for N<=3, which is inherited from a finite volume self-duality of the 2d N-state Potts models. The form of the duality as a discrete Fourier transform over ensembles with interfaces emphasizes the link between confinement and topology in pure SU(N) gauge theories.
We then investigate monopole inducing boundary conditions in SU(N) grand unified theories with an adjoint Higgs field, and find that non-trivial magnetic charge may be enforced but with several restrictions.
Finally, we introduce dynamical quarks and the curious connection between confinement and their fractional electric charge. Owing to a coincidence of quantum numbers in the matter sector, the Standard Model possesses a hidden global center symmetry that is lost when Quantum Chromodynamics (QCD) is treated as an isolated theory. We discuss the topological implications of this symmetry, and investigate their influence on the phase structure of a 2-color lattice model with quarks that carry also a fractional electric charge.