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1
ZWIEBACH, BARTON. "INTERPOLATING STRING FIELD THEORIES." Modern Physics Letters A 07, no. 12 (April 20, 1992): 1079–90. http://dx.doi.org/10.1142/s0217732392000951.
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A minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten’s open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles.
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RANDJBAR-DAEMI, S., ABDUS SALAM, and J. A. STRATHDEE. "σ-MODELS AND STRING THEORIES." International Journal of Modern Physics A 02, no. 03 (June 1987): 667–93. http://dx.doi.org/10.1142/s0217751x87000247.
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The propagation of closed bosonic strings interacting with background gravitational and dilaton fields is reviewed. The string is treated as a quantum field theory on a compact 2-dimensional manifold. The question is posed as to how the conditions for the vanishing trace anomaly and the ensuing background field equations may depend on global features of the manifold. It is shown that to the leading order in σ-model perturbation theory the string loop effects do not modify the gravitational and the dilaton field equations. However for the purely bosonic strings new terms involving the modular parameter of the world sheet are induced by quantum effects which can be absorbed into a re-definition of the background fields. We also discuss some aspects of several regularization schemes such as dimensional, Pauli-Villars and the proper-time cut off in an appendix.
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TORRIELLI, ALESSANDRO. "UNITARITY OF NONCOMMUTATIVE FIELD THEORIES FROM STRING THEORY." Modern Physics Letters A 18, no. 33n35 (November 20, 2003): 2525–32. http://dx.doi.org/10.1142/s0217732303012775.
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We improve the study of the lack of perturbative unitarity of noncommutative space-time quantum field theories derived from open string theory in electric backgrounds, enforcing the universality of the mechanism by which a tachyonic branch cut appears when the Seiberg-Witten limit freezes the string in an unstable vacuum. The main example is realized in the context of the on-shell four-tachyon amplitude of the bosonic string, and the dependence of the phenomenon on the brane-worldvolume dimension is analysed. We discuss the possibility of a proof in superstring theory, and finally mention the NCOS limit in this framework.
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Sanchez, N. G. "Advances in String Theory in Curved Backgrounds: A Synthesis Report." International Journal of Modern Physics A 18, no. 12 (May 10, 2003): 2011–22. http://dx.doi.org/10.1142/s0217751x0301543x.
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A synthetic report of the advances in the study of classical and quantum string dynamics in curved backgrounds is provided, namely : the new feature of Multistring solutions; the mass spectrum of Strings in Curved backgrounds; The effect of a Cosmological Constant and of Spacial Curvature on Classical and Quantum Strings; Classical splitting of Fundamental Strings; The General String Evolution in constant Curvature Spacetimes; The Conformal Invariance Effects; Strings on plane fronted and gravitational shock waves, string falling on spacetime singularities and its spectrum. New Developments in String Gravity and String Cosmology are reported: String driven cosmology and its Predictions; The primordial gravitational wave background; Non-singular string cosmologies from Exact Conformal Field Theories; Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time; Hawking Radiation in String Theory and the String Phase of Black Holes; New Dual Relation between Quantum Field Theory regime and String regime and the "QFT/String Tango"; New Coherent String States and Minimal Uncertainty Principle in string theory.
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HOLTEN, J. W. VAN. "BRST FIELD THEORY OF RELATIVISTIC PARTICLES." International Journal of Modern Physics A 07, no. 28 (November 10, 1992): 7119–34. http://dx.doi.org/10.1142/s0217751x92003276.
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A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. We discuss their quantization, gauge fixing and the derivation of propagators. We show, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same phenomenon holds in string theories. In particular it is shown, that the naive BRST formulation of the BDHP theory leads to trivial quantum field theories with vanishing correlation functions.
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KRÓL, JERZY. "TOPOS THEORY AND SPACETIME STRUCTURE." International Journal of Geometric Methods in Modern Physics 04, no. 02 (March 2007): 297–303. http://dx.doi.org/10.1142/s0219887807002028.
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According to the recently proposed model of spacetime, various difficulties of quantum field theories and semiclassical quantum gravity on curved 4-Minkowski spacetimes gain new formulations, leading to new solutions. The quantum mechanical effects appear naturally when diffeomorphisms are lifted to 2-morphisms between topoi. The functional measures can be well defined. Diffeomorphisms invariance and background independence are approached from the perspective of topoi. In the spacetimes modified at short distances by the internal structure of some topoi, the higher dimensional regions appear and field/strings duality emerges. We show that the model has natural extensions over extremely strong gravity sources in spacetime and shed light on the strong string coupling definition of B-type D-branes.
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HATSUDA, MACHIKO. "BRST FIELD THEORIES FOR A QUANTUM LORENTZ PARTICLE." International Journal of Modern Physics A 07, no. 06 (March 10, 1992): 1187–213. http://dx.doi.org/10.1142/s0217751x9200051x.
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From the study of string field theory, first quantized BRST symmetry is known to be a guiding principle in constructing field theories. We construct the first quantized BRST charge QB for a quantum Lorentz particle which is characterized by the constraints which are expressed in terms of (inhomogeneous) Lorentz generators. It is shown that the BRST cohomology of this system includes only the field strengths and not the fundamental gauge fields with nontrivial norms. By using this BRST charge, we obtain the field theory Lagrangian via the ∫ΨQBΨ construction, which leads to field equations for fields with arbitrary spin. However, this action cannot be used to derive a second quantized theory except for Dirac fields. For antisymmetric tensor fields, we can get the correct second quantized theories if we introduce extra conditions.
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YONEYA, TAMIAKI. "SPACE-TIME UNCERTAINTY AND NONCOMMUTATIVITY IN STRING THEORY." International Journal of Modern Physics A 16, no. 05 (February 20, 2001): 945–55. http://dx.doi.org/10.1142/s0217751x01004025.
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We analyze the nature of space-time nonlocality in string theory. After giving a brief overview on the conjecture of the space-time uncertainty principle, a (semi-classical) reformulation of string quantum mechanics, in which the dynamics is represented by the noncommutativity between temporal and spatial coordinates, is outlined. The formalism is then compared to the space-time noncommutative field theories associated with nonzero electric B-fields.
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SHEIKH-JABBARI, M. M. "NONCOMMUTATIVE OPEN STRING THEORIES AND THEIR DUALITIES." Modern Physics Letters A 16, no. 04n06 (February 28, 2001): 349–59. http://dx.doi.org/10.1142/s0217732301003450.
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The recently found noncritical open string theories is reviewed. These open strings, noncommutative open string theories (NCOS), arise as consistent quantum theories describing the low energy theory of D-branes in a background electric B-field in the critical limit. Focusing on the D3-brane case, we construct the most general (3+1) NCOS, which is described by four parameters. We study S- and T-dualities of these theories and argue the existence of a U-duality group.
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MARSHAKOV, A. "EXACT SOLUTIONS TO QUANTUM FIELD THEORIES AND INTEGRABLE EQUATIONS." Modern Physics Letters A 11, no. 14 (May 10, 1996): 1169–83. http://dx.doi.org/10.1142/s021773239600120x.
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The exact solutions to quantum string and gauge field theories are discussed and their formulation in the framework of integrable systems is presented. In particular we consider in detail several examples of the appearance of solutions to the first-order integrable equations of hydrodynamical type and stress that all known examples can be treated as partial solutions to the same problem in the theory of integrable systems.
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YAMAGUCHI, YOSHIO. "QUANTUM FIELD THEORIES OF STRONG INTERACTIONS." Modern Physics Letters A 25, no. 17 (June 7, 2010): 1403–5. http://dx.doi.org/10.1142/s0217732310033128.
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Strong interactions are described by the Quantum Field Theory due to Heisenberg–Pauli. We postulate that the one particle physical states with appropriate quantum numbers (fermions and bosons) must be expressed by the normalized Fock space state vectors, which can conveniently be (and approximately) calculated in their rest frame, using Tamm–Dancoff variational method. Interactions between two physical particles can be analyzed by the same Hamiltonian as for each physical particle state, similar to analyzing nucleus–nucleus collisions. Our theories are free from any ultraviolet divergency. Our one physical particle state is similar to bound state in quantum mechanics.
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DEMETERFI, KREŠIMIR. "TWO-DIMENSIONAL QUANTUM GRAVITY, MATRIX MODELS AND STRING THEORY." International Journal of Modern Physics A 08, no. 07 (March 20, 1993): 1185–244. http://dx.doi.org/10.1142/s0217751x93000497.
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We review some results of the recent progress in understanding two-dimensional quantum gravity and low-dimensional string theories based on the lattice approach. The possibility to solve the lattice models exactly comes from their equivalence to large N matrix models. We describe various matrix models and their continuum limits, and discuss in some detail the phase structure of Hermitian one-matrix models. For the one-dimensional matrix model we discuss its field theoretic formulation through a collective field method and summarize some perturbative results. We compare the results obtained from matrix models to the results in the continuum approach to string theory.
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ROBERTSON, DAVID G. "ANISOTROPIC SCALING IN RELATIVISTIC FIELD THEORY." International Journal of Modern Physics A 06, no. 20 (August 20, 1991): 3643–69. http://dx.doi.org/10.1142/s0217751x91001775.
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We study the behavior of relativistic quantum field theories under anisotropic scale transformations, of the general form pμ→σμvpv, where σμv are a set of constant scale parameters. We derive, for an arbitrary theory, the linear response to such a transformation, and show how this may be used to determine the renormalization group flow of the anisotropic effective theory. Some applications of the formalism are suggested, including a possible strategy for motivating phenomenological string models of hadrons, starting from microscopic QCD.
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Zhou, Zhao-Yu, Guo-Xian Su, Jad C. Halimeh, Robert Ott, Hui Sun, Philipp Hauke, Bing Yang, Zhen-Sheng Yuan, Jürgen Berges, and Jian-Wei Pan. "Thermalization dynamics of a gauge theory on a quantum simulator." Science 377, no. 6603 (July 15, 2022): 311–14. http://dx.doi.org/10.1126/science.abl6277.
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Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems. We perform quantum simulations of the unitary dynamics of a U(1) symmetric gauge field theory and demonstrate emergent irreversible behavior. The highly constrained gauge theory dynamics are encoded in a one-dimensional Bose-Hubbard simulator, which couples fermionic matter fields through dynamical gauge fields. We investigated global quantum quenches and the equilibration to a steady state well approximated by a thermal ensemble. Our work may enable the investigation of elusive phenomena, such as Schwinger pair production and string breaking, and paves the way for simulating more complex, higher-dimensional gauge theories on quantum synthetic matter devices.
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LU, H., X. J. WANG, K. W. XU, C. N. POPE, and K. THIELEMANS. "QUANTIZING HIGHER-SPIN STRING THEORIES." International Journal of Modern Physics A 10, no. 14 (June 10, 1995): 2123–42. http://dx.doi.org/10.1142/s0217751x95001030.
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In this paper, we examine the conditions under which a higher-spin string theory can be quantized. The quantizability is crucially dependent on the way in which the matter currents are realized at the classical level. In particular, we construct classical realizations for the W2,s algebra, which is generated by a primary spin-s current in addition to the energy-momentum tensor, and discuss the quantization for s≤8. From these examples we see that quantum BRST operators can exist even when there is no quantum generalization of the classical W2,s algebra. Moreover, we find that there can be several inequivalent ways of quantizing a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already known W strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalizations lead us to examine whether classical BRST operators for [Formula: see text](n odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.
16
Krasnikov, N. V. "Quantum field theory with infinite component local fields as an alternative to the string theories." Physics Letters B 195, no. 3 (September 1987): 377–81. http://dx.doi.org/10.1016/0370-2693(87)90035-9.
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Jordan, Stephen P., Keith S. M. Lee, and John Preskill. "Quantum computation of scattering in scalar quantum field theories." Quantum Information and Computation 14, no. 11&12 (September 2014): 1014–80. http://dx.doi.org/10.26421/qic14.11-12-8.
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Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive $\phi^4$ theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.
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He, Yang-Hui. "Quiver Gauge Theories: Finitude and Trichotomoty." Mathematics 6, no. 12 (November 28, 2018): 291. http://dx.doi.org/10.3390/math6120291.
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D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of standard techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, conformality and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then, we utilise certain results from graph theory and axiomatic representation theory of path algebras to address physical issues such as the implication of graph additivity to finiteness of gauge theories, the impossibility of constructing completely IR free string orbifold theories and the unclassifiability of N < 2 Yang-Mills theories in four dimensions.
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de Lacroix, Corinne, Harold Erbin, Sitender Pratap Kashyap, Ashoke Sen, and Mritunjay Verma. "Closed superstring field theory and its applications." International Journal of Modern Physics A 32, no. 28n29 (October 19, 2017): 1730021. http://dx.doi.org/10.1142/s0217751x17300216.
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We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 noncompact space–time dimensions, but suffers from the usual infrared divergences when the number of noncompact space–time dimensions is 4 or less.
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Marathe, Kishore. "Quantum theories and geometric topology: A chapter in physical mathematics." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460024. http://dx.doi.org/10.1142/s021988781460024x.
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In recent years, the interaction between geometric topology and classical and quantum field theories has attracted a great deal of attention from both the mathematicians and physicists. We discuss some topics from low-dimensional topology where this has led to new viewpoints as well as new results. They include categorification of knot polynomials and a special case of the gauge theory to string theory correspondence in the Euclidean version of the theories, where exact results are available. We show how the Witten–Reshetikhin–Turaev invariant in SU (n) Chern–Simons theory on S3 is related via conifold transition to the all-genus generating function of the topological string amplitudes on a Calabi–Yau manifold. This result can be thought of as an interpretation of TQFT as topological quantum gravity (TQG). After a brief discussion of Perelman's work on the geometrization conjecture and its relation to gravity, we comment on some recent work on black hole radiation and its relation to mock moonshine.
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Kan, Nahomi, Masashi Kuniyasu, and Kiyoshi Shiraishi. "Quantum fluctuation of stress tensor in a higher-derivative scalar field theory around a cosmic string." International Journal of Modern Physics A 36, no. 20 (July 9, 2021): 2150150. http://dx.doi.org/10.1142/s0217751x21501505.
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In this paper, we calculate the vacuum fluctuation of the stress tensor of a higher-derivative theory around a thin cosmic string. To this end, we adopt the method to obtain the stress tensor from the effective action developed by Gibbons et al. By their method, the quantum stress tensor of higher-derivative scalar theories without self-interaction is expressed as a simple sum of quantum stress tensors of free massive scalar fields. Unlike the vacuum expectation value of the scalar field squared obtained in the similar model, there appears no reduction of the values near the conical singularity.
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Singh, Tejinder P. "Outline for a Quantum Theory of Gravity." Zeitschrift für Naturforschung A 74, no. 5 (May 27, 2019): 383–86. http://dx.doi.org/10.1515/zna-2019-0027.
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AbstractBy invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four-dimensional non-commutative curvature scalar (which is torsion dependent), which is sourced by the Nambu–Goto world-sheet action for a string plus the Kalb–Ramond string action. This ‘quantum gravity’ is actually a non-commutative classical matrix dynamics, and the only two fundamental constants in the theory are the square of the Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and ℏ) and quantum general relativity (and G) emerge from the underlying matrix dynamics in the thermodynamic limit. Statistical fluctuations, which are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope to highlight here the deep connection between quantum foundations and the sought-for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!
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Durand, Philippe. "Mathematical Tools to Understand the Field Theories of the Standard Model and Beyond." International Journal of Mathematics and Computers in Simulation 15 (July 28, 2021): 54–61. http://dx.doi.org/10.46300/9102.2021.15.10.
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Since Isaac Newton the understanding of the physical world is more and more complex. The Euclidean space of three dimensions , independent of time is replaced in Enstein’s vision by the Lorentzian space-time at first, then by four dimensions manifold to unify space and matter. String theorists add to space more dimensions to make their theory consistent. Complex topological invariants which characterize different kind of spaces are developed. Space is discretized at the quantum scale in the loop quantum gravity theory. A non-commutative and spectral geometry is defined from the theory of operator algebra by Alain Connes. In this review, our goal is to enumerate different approaches implementing algebra and topology in order to understand the standard model of particles and beyond
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KIMURA, TETSUJI. "INDEX THEOREMS ON TORSIONAL GEOMETRIES." International Journal of Modern Physics A 23, no. 14n15 (June 20, 2008): 2260–61. http://dx.doi.org/10.1142/s0217751x08041001.
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We investigate the Atiyah-Singer index theorems with torsion given by Neveu-Schwarz three-form flux H under the condition d H = 0 in flux compactification scenarios with non-trivial background fields in string theories. Using an identification between the Clifford algebra on the geometry and the canonical quantization condition in [Formula: see text] quantum mechanics, we explicitly reformulate the Dirac index on manifolds with torsion, which will provides a fundamental information to effective theories derived from string theory. In the same analogy we also reformulate the Euler characteristics and the Hirzebruch signatures in the framework of [Formula: see text] quantum mechanics.
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CASTRO, CARLOS. "ON THE LARGE N LIMIT, WILSON LOOPS, CONFINEMENT AND COMPOSITE ANTISYMMETRIC TENSOR FIELD THEORIES." International Journal of Modern Physics A 19, no. 25 (October 10, 2004): 4251–70. http://dx.doi.org/10.1142/s0217751x04019718.
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A novel approach to evaluate the Wilson loops associated with a SU (∞) gauge theory in terms of pure string degrees of freedom is presented. It is based on the Guendelman–Nissimov–Pacheva formulation of composite antisymmetric tensor field theories of area (volume) preserving diffeomorphisms which admit p-brane solutions and which provide a new route to scale-symmetry breaking and confinement in Yang–Mills theory. The quantum effects are discussed and we evaluate the vacuum expectation values (VEV) of the Wilson loops in the large N limit of the quenched reduced SU (N) Yang–Mills theory in terms of a path integral involving pure string degrees of freedom. The quenched approximation is necessary to avoid a crumpling of the string worldsheet giving rise to very large Hausdorff dimensions as pointed out by Olesen. The approach is also consistent with the recent results based on the AdS/CFT correspondence and dual QCD models (dual Higgs model with dual Dirac strings). More general Loop wave equations in C-spaces (Clifford manifolds) are proposed in terms of generalized holographic variables that contain the dynamics of an aggregate of closed branes (p-loops) of various dimensionalities. This allows us to construct the higher-dimensional version of Wilson loops in terms of antisymmetric tensor fields of arbitrary rank which couple to p-branes of different dimensionality.
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HABARA, YOSHINOBU, YUKINORI NAGATANI, HOLGER B. NIELSEN, and MASAO NINOMIYA. "DIRAC SEA AND HOLE THEORY FOR BOSONS I: A NEW FORMULATION OF QUANTUM FIELD THEORIES." International Journal of Modern Physics A 23, no. 18 (July 20, 2008): 2733–69. http://dx.doi.org/10.1142/s0217751x08040342.
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Bosonic formulation of the negative energy sea, so-called Dirac sea, is proposed by constructing a hole theory for bosons as a new formulation of the second quantization of bosonic fields. The original idea of Dirac sea for fermions, where the vacuum state is considered as a state completely filled by fermions of negative energy and holes in the sea are identified as antiparticles, is extended to boson case in a consistent manner. The bosonic vacuum consists of a sea filled by negative energy bosonic states, while physical probabilities become always positive definite. We introduce a method of the double harmonic oscillator to formulate the hole theory of bosons. Our formulation is also applicable to supersymmetric field theory. The sea for supersymmetric theories has an explicit supersymmetry. We suggest applications of our formulations to the anomaly theories and the string theories.
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WOON, S. C. "ANALYTIC CONTINUATION OF OPERATORS APPLICATIONS: FROM NUMBER THEORY AND GROUP THEORY TO QUANTUM FIELD AND STRING THEORIES." Reviews in Mathematical Physics 11, no. 04 (April 1999): 463–501. http://dx.doi.org/10.1142/s0129055x99000179.
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We are used to thinking of an operator acting once, twice, and so on. However, an operator can be analytically continued to the operator raised to a complex power. Applications include (s,r) diagrams and an extension of Fractional Calculus where commutativity of fractional derivatives is preserved, generating integrals and non-standard derivations of theorems in Number Theory, non-integer power series and breaking of Leibniz and Chain rules, pseudo-groups and symmetry deforming models in particle physics and cosmology, non-local effect in analytically continued matrix representations and its connection with noncommutative geometry, particle-physics-like scatterings of zeros of analytically continued Bernoulli polynomials, and analytic continuation of operators in QM, QFT and Strings.
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Boi, Luciano. "Geometrical and topological foundations of theoretical physics: from gauge theories to string program." International Journal of Mathematics and Mathematical Sciences 2004, no. 34 (2004): 1777–836. http://dx.doi.org/10.1155/s0161171204304400.
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We study the role of geometrical and topological concepts in the recent developments of theoretical physics, notably in non-Abelian gauge theories and superstring theory, and further we show the great significance of these concepts for a deeper understanding of the dynamical laws of physics. This work aims to demonstrate that the global topological properties of the manifold's model of spacetime play a major role in quantum field theory and that, therefore, several physical quantum effects arise from the nonlocal metrical and topological structure of this manifold. We mathematically argue the need for building new structures of space with different topology. This means, in particular, that the hidden symmetries of fundamental physics can be related to the phenomenon of topological change of certain classes of (presumably) nonsmooth manifolds.
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GRAHAM, NOAH, ROBERT L. JAFFE, and HERBERT WEIGEL. "CASIMIR EFFECTS IN RENORMALIZABLE QUANTUM FIELD THEORIES." International Journal of Modern Physics A 17, no. 06n07 (March 20, 2002): 846–69. http://dx.doi.org/10.1142/s0217751x02010224.
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We present a framework for the study of one–loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
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CASTRO, CARLOS. "ON OCTONIONIC GRAVITY, EXCEPTIONAL JORDAN STRINGS AND NONASSOCIATIVE TERNARY GAUGE FIELD THEORIES." International Journal of Geometric Methods in Modern Physics 09, no. 03 (May 2012): 1250021. http://dx.doi.org/10.1142/s0219887812500211.
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Novel nonassociative octonionic ternary gauge field theories are proposed based on a ternary bracket. This paves the way to the many physical applications of exceptional Jordan Strings/Membranes and Octonionic Gravity. The old octonionic gravity constructions based on the split octonion algebra Os (which strictly speaking is not a division algebra) is extended to the full fledged octonion division algebra O. A real-valued analog of the Einstein–Hilbert Lagrangian [Formula: see text] involving sums of all the possible contractions of the Ricci tensors plus their octonionic-complex conjugates is presented. A discussion follows of how to extract the Standard Model group (the gauge fields) from the internal part of the octonionic gravitational connection. The role of exceptional Jordan algebras, their automorphism and reduced structure groups which play the roles of the rotation and Lorentz groups is also re-examined. Finally, we construct (to our knowledge) generalized novel octonionic string and p-brane actions and raise the possibility that our generalized 3-brane action (based on a quartic product) in octonionic flat backgrounds of 7,8 octonionic dimensions may display an underlying E7, E8 symmetry, respectively. We conclude with some final remarks pertaining to the developments related to Jordan exceptional algebras, octonions, black-holes in string theory and quantum information theory.
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Kamau-Devers, Gathoni, Gail Jardine, and David Yetter. "A general state-sum construction of 2-dimensional topological quantum field theories with defects." Journal of Knot Theory and Its Ramifications 26, no. 04 (April 2017): 1750014. http://dx.doi.org/10.1142/s0218216517500146.
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We derive a general state sum construction for 2D topological quantum field theories (TQFTs) with source defects on oriented curves, extending the state-sum construction from special symmetric Frobenius algebra for 2D TQFTs without defects (cf. Lauda and Pfeiffer [State-sum construction of two-dimensional open-closed topological quantum field theories, J. Knot Theory Ramifications 16 (2007) 1121–1163, doi: 10.1142/S0218216507005725]). From the extended Pachner moves (Crane and Yetter [Moves on filtered PL manifolds and stratified PL spaces, arXiv:1404.3142 ]), we derive equations that we subsequently translate into string diagrams so that we can easily observe their properties. As in Dougherty, Park and Yetter [On 2-dimensional Dijkgraaf–Witten theory with defects, to appear in J. Knots Theory Ramifications], we require that triangulations be flaglike, meaning that each simplex of the triangulation is either disjoint from the defect curve, or intersects it in a closed face, and that the extended Pachner moves preserve flaglikeness.
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Halimeh, Jad C., Maarten Van Damme, Torsten V. Zache, Debasish Banerjee, and Philipp Hauke. "Achieving the quantum field theory limit in far-from-equilibrium quantum link models." Quantum 6 (December 19, 2022): 878. http://dx.doi.org/10.22331/q-2022-12-19-878.
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Realizations of gauge theories in setups of quantum synthetic matter open up the possibility of probing salient exotic phenomena in condensed matter and high-energy physics, along with potential applications in quantum information and science technologies. In light of the impressive ongoing efforts to achieve such realizations, a fundamental question regarding quantum link model regularizations of lattice gauge theories is how faithfully they capture the quantum field theory limit of gauge theories. Recent work \cite{zache2021achieving} has shown through analytic derivations, exact diagonalization, and infinite matrix product state calculations that the low-energy physics of 1+1D U(1) quantum link models approaches the quantum field theory limit already at small link spin length S. Here, we show that the approach to this limit also lends itself to the far-from-equilibrium quench dynamics of lattice gauge theories, as demonstrated by our numerical simulations of the Loschmidt return rate and the chiral condensate in infinite matrix product states, which work directly in the thermodynamic limit. Similar to our findings in equilibrium that show a distinct behavior between half-integer and integer link spin lengths, we find that criticality emerging in the Loschmidt return rate is fundamentally different between half-integer and integer spin quantum link models in the regime of strong electric-field coupling. Our results further affirm that state-of-the-art finite-size ultracold-atom and NISQ-device implementations of quantum link lattice gauge theories have the real potential to simulate their quantum field theory limit even in the far-from-equilibrium regime.
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Heidenreich, Ben, Matthew Reece, and Tom Rudelius. "Axion experiments to algebraic geometry: Testing quantum gravity via the Weak Gravity Conjecture." International Journal of Modern Physics D 25, no. 12 (October 2016): 1643005. http://dx.doi.org/10.1142/s0218271816430057.
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Common features of known quantum gravity theories may hint at the general nature of quantum gravity. The absence of continuous global symmetries is one such feature. This inspired the Weak Gravity Conjecture, which bounds masses of charged particles. We propose the Lattice Weak Gravity Conjecture, which further requires the existence of an infinite tower of particles of all possible charges under both abelian and nonabelian gauge groups and directly implies a cutoff for quantum field theory. It holds in a wide variety of string theory examples and has testable consequences for the real world and for pure mathematics. We sketch some implications of these ideas for models of inflation, for the QCD axion (and LIGO), for conformal field theory, and for algebraic geometry.
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Güijosa, Alberto. "QCD, with strings attached." International Journal of Modern Physics E 25, no. 10 (October 2016): 1630006. http://dx.doi.org/10.1142/s021830131630006x.
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In the nearly 20 years that have elapsed since its discovery, the gauge-gravity correspondence has become established as an efficient tool to explore the physics of a large class of strongly-coupled field theories. A brief overview is given here of its formulation and a few of its applications, emphasizing attempts to emulate aspects of the strong-coupling regime of quantum chromodynamics (QCD). To the extent possible, the presentation is self-contained, and does not presuppose knowledge of string theory.
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Ellis, John, N. E. Mavromatos, and D. V. Nanopoulos. "D Branes from Liouville Strings." International Journal of Modern Physics A 12, no. 15 (June 20, 1997): 2639–73. http://dx.doi.org/10.1142/s0217751x97001481.
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We develop quantization aspects of our Liouville approach to noncritical strings, proposing a path-integral formulation of a second quantization of string theory, that incorporates naturally the couplings of string sources to background fields. Such couplings are characteristic of macroscopic string solutions and/or D-brane theories. Resummation over world-sheet genera in the presence of stringy (σ-model) soliton backgrounds, and recoil effects associated with logarithmic operators on the world sheet, play a crucial role in inducing such sources as well-defined renormalization-group counterterms. Using our Liouville renormalization group approach, we derive the appropriate second-order equation of motion for the D brane. We discuss within this approach the appearance of open strings, whose ends carry nontrivial Chan–Paton-like quantum numbers related to the W∞ charges of two-dimensional string black holes.
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SCHWARZ, JOHN H. "SUPERCONFORMAL SYMMETRY AND SUPERSTRING COMPACTIFICATION." International Journal of Modern Physics A 04, no. 11 (July 10, 1989): 2653–713. http://dx.doi.org/10.1142/s0217751x89001035.
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Various topics in conformal field theory and the theory of Kac-Moody algebras are presented. In particular, the Goddard-Kent-Olive construction is used to derive various conformal and superconformal theories, including a large class of N=2 models recently discovered by Kazama and Suzuki. The relationship between compactification of extra dimensions and the description of internal degrees of freedom by a conformal field theory is discussed. Various approaches to compactification based on exactly soluble conformal field theories, including Gepner’s proposal for using the N=2 minimal models, are sketched. Recent progress in understanding N=2 models and Calabi-Yau spaces using mathematical techniques of singularity theory is described. It is argued that a classical solution could be a useful first approximation to a quantum ground state even though it is known that string theory is strongly coupled and the perturbation expansion diverges.
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Anastasopoulos, Pascal. "Emergent fields from hidden sectors." Journal of Physics: Conference Series 2105, no. 1 (November 1, 2021): 012002. http://dx.doi.org/10.1088/1742-6596/2105/1/012002.
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Abstract The present research proceeding aims at investigating/exploring/sharpening the phenomenological consequences of string theory and holography in particle physics and cosmology. We rely on and elaborate on the recently proposed framework whereby four-dimensional quantum field theories describe all interactions in Nature, and gravity is an emergent and not a fundamental force. New gauge fields, axions, and fermions, which can play the role of right-handed neutrinos, can also emerge in this framework. Preprint: UWThPh 2021-8
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Corrigan, Edward, and Peter Goddard. "David Ian Olive. 16 April 1937—7 November 2012." Biographical Memoirs of Fellows of the Royal Society 69 (September 16, 2020): 467–98. http://dx.doi.org/10.1098/rsbm.2020.0024.
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David Olive, who died in Barton, Cambridgeshire, on 7 November 2012, aged 75, was a theoretical physicist who made seminal contributions to the development of string theory and to our understanding of the structure of quantum field theory. In early work on S -matrix theory, he helped to provide the conceptual framework within which string theory was initially formulated. His work, with Gliozzi and Scherk, on supersymmetry in string theory made possible the whole idea of superstrings, now understood as the natural framework for string theory. Olive’s pioneering insights about the duality between electric and magnetic objects in gauge theories were way ahead of their time; it took two decades before his bold and courageous duality conjectures began to be understood. Although somewhat quiet and reserved, he took delight in the company of others, generously sharing his emerging understanding of new ideas with students and colleagues. He was widely influential, not only through the depth and vision of his original work, but also because the clarity, simplicity and elegance of his expositions of new and difficult ideas and theories provided routes into emerging areas of research, both for students and for the theoretical physics community more generally.
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MARINO, E. C. "CREATION OPERATORS FOR TWO-BRANES AND DUALITY IN BF AND CHERN–SIMONS THEORIES IN D=5." International Journal of Modern Physics A 18, no. 32 (December 30, 2003): 5907–20. http://dx.doi.org/10.1142/s0217751x03016781.
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We explicitly construct the creation operators for the quantum field configurations associated to quantum membranes (two-branes) in BF and generalized Chern–Simons theories in a space–time of dimension D=5. The creation operators for quantum excitations carrying topological charge are also obtained in the same theories. For the case of D=5 generalized Chern–Simons theory, we show that this operator actually creates an open string with a topological charge at its tip. It is shown that a duality structure exists in general, relating the membrane and topological excitation operators and the corresponding dual algebra is derived. Composite topologically charged membranes are shown to possess generalized statistics that may, in particular, be fermionic. This is the first step for the bosonization procedure in these theories. Potential applications in the full quantization of two-branes is also briefly discussed.
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MANOUKIAN, E. B., and N. YONGRAM. "POLARIZATION CORRELATIONS IN PAIR PRODUCTION FROM CHARGED AND NEUTRAL STRINGS." Modern Physics Letters A 20, no. 08 (March 14, 2005): 623–28. http://dx.doi.org/10.1142/s0217732305015847.
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Polarization correlations of e+e- pair productions from charged and neutral Nambu strings are investigated, via photon and graviton emissions, respectively and explicit expressions for their corresponding probabilities are derived and found to be speed dependent. The strings are taken to be circularly oscillating closed strings, as perhaps the simplest solution of the Nambu action. In the extreme relativistic case, these probabilities coincide, but, in general, are different, and such inquiries, in principle, indicate whether the string is charged or uncharged. It is remarkable that these dynamical relativistic quantum field theory calculations lead to a clear violation of Local Hidden Variables theories.
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WATANABE, HIROSHI. "RENORMALIZATION GROUP METHODS IN CONSTRUCTIVE FIELD THEORIES." International Journal of Modern Physics B 14, no. 12n13 (May 30, 2000): 1363–98. http://dx.doi.org/10.1142/s0217979200001023.
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Mathematical construction of quantum field theory is reviewed with emphasis on the conceptual structure of the construction and on the role of rigorous renormalization group analysis without technical details. After explaining a rigorous formulation of a renormalization group method in a weak coupling region, a new approach in a strong coupling region is proposed in the context of the hierarchical approximation. An idea of proving triviality in d≥4 dimensions utilizing this new proposal concludes this review.
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Gölgeleyen, İsmet, and Özlem Kaytmaz. "Uniqueness for a Cauchy problem for the generalized Schrödinger equation." AIMS Mathematics 8, no. 3 (2022): 5703–24. http://dx.doi.org/10.3934/math.2023287.
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<abstract><p>In this work, we consider a Cauchy problem for the generalized Schrö dinger equation which has important applications in quantum kinetic theory, water wave problems and ferromagnetism. Due to its multidimensionality, it is important from the point of view of modern physics theories such as quantum field theory and string theory. We prove the uniqueness of the solution of the problem in an unbounded domain by using semigeodesic coordinates. The main tool is a pointwise Carleman estimate. To the authors' best knowledge, this is the first study which deals with the solvability of this problem.</p></abstract>
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BASEILHAC, P., P. GRANGÉ, and V. A. FATEEV. "EXACT DUALITY BETWEEN INTEGRABLE DEFORMATIONS OF BCn AND $C_n^{(1)}$ AFFINE TODA THEORIES." Modern Physics Letters A 13, no. 12 (April 20, 1998): 937–51. http://dx.doi.org/10.1142/s0217732398001017.
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Integrable deformations of two affine Toda field theories based on BCn and [Formula: see text] non-simply laced algebras are studied. The proof of quantum integrability of the two theories is given and it is shown that the two theories are dual, corresponding respectively to the weak and strong coupling regimes of an intermediate theory. Perturbative calculations and the bootstrap principle permit the construction of the intermediate quantum field theory which flows from the first to the second with the coupling constant.
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GONCHAROV, YU P. "TOPOLOGICAL DUALITY BETWEEN REAL SCALAR AND SPINOR FIELDS IN QUANTUM FIELD THEORY, COSMOLOGY, QUANTUM THEORIES OF FUNDAMENTAL EXTENDED OBJECTS." International Journal of Modern Physics A 09, no. 01 (January 10, 1994): 1–37. http://dx.doi.org/10.1142/s0217751x94000029.
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This survey is devoted to possible manifestations of remarkable topological duality between real scalar and spinor fields (TDSS) existing on a great number of manifolds important in physical applications. The given manifestations are demonstrated to occur within the framework of miscellaneous branches in ordinary and supersymmetric quantum field theories, supergravity, Kaluza-Klein type theories, cosmology, strings, membranes and p-branes. All this allows one to draw the condusion that the above duality will seem to be an essential ingredient in many questions of present and future investigations.
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WITTEN, EDWARD. "ANTI-DE SITTER SPACE, THERMAL PHASE TRANSITION AND CONFINEMENT IN GAUGE THEORIES." International Journal of Modern Physics A 16, no. 16 (June 30, 2001): 2747–69. http://dx.doi.org/10.1142/s0217751x01004451.
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.
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DAS, SUMIT R., AVINASH DHAR, and SPENTA R. WADIA. "CRITICAL BEHAVIOR IN TWO-DIMENSIONAL QUANTUM GRAVITY AND EQUATIONS OF MOTION OF THE STRING." Modern Physics Letters A 05, no. 11 (May 10, 1990): 799–813. http://dx.doi.org/10.1142/s0217732390000895.
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We show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. We discuss an example of such a trajectory in the space containing the c < 1 minimal models. We also discuss the connection between this work and the recent attempts to construct non-perturbative string theories based on matrix models.
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Nassar, Ali, and Mark A. Walton. "Rational conformal field theory with matrix level and strings on a torus." Canadian Journal of Physics 92, no. 1 (January 2014): 65–70. http://dx.doi.org/10.1139/cjp-2013-0326.
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Study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of Um,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes it obvious that the rational theories are dense in the moduli space of strings on Tm, and may prove useful in other ways.
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Kassem, Ayman. "Main Title: Quanton Based Model of Field Interactions,." JOURNAL OF ADVANCES IN PHYSICS 20 (May 4, 2022): 110–39. http://dx.doi.org/10.24297/jap.v20i.9217.
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The search for a unification of the physical phenomena was the preoccupation of many physicists for long time. Starting from the seventeenth century with the unification of celestial mechanics and gravitation, then the unification of the electromagnetism in the nineteenth century. The early twentieth century brought about the unification of space and time and the unification of energy and mass while the advent of gauge theory enabled the unification of the weak interaction with the electromagnetism in the middle of the twentieth century. More recent theories are proposed as the answer to the unification question in physics include quantum gravity which unifies quantum mechanics and gravitation, and string theory. Unification effort should not only address the known fundamental forces but the space fabric interactions which till now remain unknown but their manifestations are described as the dark energy and dark matter. Here the concept of interacting space and time fields which constitute space time is discussed using classic method which has a certain advantage of bringing the physical meaning into visualization.
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BOI, LUCIANO. "IDEAS OF GEOMETRIZATION, GEOMETRIC INVARIANTS OF LOW-DIMENSIONAL MANIFOLDS, AND TOPOLOGICAL QUANTUM FIELD THEORIES." International Journal of Geometric Methods in Modern Physics 06, no. 05 (August 2009): 701–57. http://dx.doi.org/10.1142/s0219887809003783.
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The aim of the first part of this paper is to make some reflections on the role of geometrical and topological concepts in the developments of theoretical physics, especially in gauge theory and string theory, and we show the great significance of these concepts for a better understanding of the dynamics of physics. We will claim that physical phenomena essentially emerge from the geometrical and topological structure of space–time. The attempts to solve one of the central problems in 20th theoretical physics, i.e. how to combine gravity and the other forces into an unitary theoretical explanation of the physical world, essentially depends on the possibility of building a new geometrical framework conceptually richer than Riemannian geometry. In fact, it still plays a fundamental role in non-Abelian gauge theories and in superstring theory, thanks to which a great variety of new mathematical structures has emerged. The scope of this presentation is to highlight the importance of these mathematical structures for theoretical physics. A very interesting hypothesis is that the global topological properties of the manifold's model of space–time play a major role in quantum field theory (QFT) and that, consequently, several physical quantum effects arise from the nonlocal changing metrical and topological structure of these manifold. Thus the unification of general relativity and quantum theory require some fundamental breakthrough in our understanding of the relationship between space–time and quantum process. In particular the superstring theories lead to the guess that the usual structure of space–time at the quantum scale must be dropped out from physical thought. Non-Abelian gauge theories satisfy the basic physical requirements pertaining to the symmetries of particle physics because they are geometric in character. They profoundly elucidate the fundamental role played by bundles, connections, and curvature in explaining the essential laws of nature. Kaluza–Klein theories and more remarkably superstring theory showed that space–time symmetries and internal (quantum) symmetries might be unified through the introduction of new structures of space with a different topology. This essentially means, in our view, that "hidden" symmetries of fundamental physics can be related to the phenomenon of topological change of certain class of (presumably) nonsmooth manifolds. In the second part of this paper, we address the subject of topological quantum field theories (TQFTs), which constitute a remarkably important meeting ground for physicists and mathematicians. TQFTs can be used as a powerful tool to probe geometry and topology in low dimensions. Chern–Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of QFTs which can be exactly (nonperturbatively) and explicitly solved. Abelian Chern–Simons theory provides a field theoretic interpretation of the linking and self-linking numbers of a link (i.e. the union of a finite number of disjoint knots). In non-Abelian theories, vacuum expectation values of Wilson link operators yield a class of polynomial link invariants; the simplest of them is the well-known Jones polynomial. Powerful methods for complete analytical and nonperturbative computation of these knot and link invariants have been developed. From these invariants for unoriented and framed links in S3, an invariant for any three-manifold can be easily constructed by exploiting the Lickorish–Wallace surgery presentation of three-manifolds. This invariant up to a normalization is the partition function of the Chern–Simons field theory. Even perturbative analysis of Chern–Simons theories are rich in their mathematical structure; these provide a field theoretic interpretation of Vassiliev knot invariants. In Donaldson–Witten theory perturbative methods have proved their relations to Donaldson invariants. Nonperturbative methods have been applied after the work by Seiberg and Witten on N = 2 supersymmetric Yang–Mills theory. The outcome of this application is a totally unexpected relation between Donaldson invariants and a new set of topological invariants called Seiberg–Witten invariants. Not only in mathematics, Chern–Simons theories find important applications in three- and four-dimensional quantum gravity also. Work on TQFT suggests that a quantum gravity theory can be formulated in three-dimensional space–time. Attempts have been made in the last years to formulate a theory of quantum gravity in four-dimensional space–time using "spin networks" and "spin foams". More generally, the developments of TQFTs represent a sort of renaissance in the relation between geometry and physics. The most important (new) feature of present developments is that links are being established between quantum physics and topology. Maybe this link essentially rests on the fact that both quantum theory and topology are characterized by discrete phenomena emerging from a continuous background. One very interesting example is the super-symmetric quantum mechanics theory, which has a deep geometric meaning. In the Witten super-symmetric quantum mechanics theory, where the Hamiltonian is just the Hodge–Laplacian (whereas the quantum Hamiltonian corresponding to a classical particle moving on a Riemannian manifold is just the Laplace–Beltrami differential operator), differential forms are bosons or fermions depending on the parity of their degrees. Witten went to introduce a modified Hodge–Laplacian, depending on a real-valued function f. He was then able to derive the Morse theory (relating critical points of f to the Betti numbers of the manifold) by using the standard limiting procedures relating the quantum and classical theories. Super-symmetric QFTs essentially should be viewed as the differential geometry of certain infinite-dimensional manifolds, including the associated analysis (e.g. Hodge theory) and topology (e.g. Betti numbers). A further comment is that the QFTs of interest are inherently nonlinear, but the nonlinearities have a natural origin, e.g. coming from non-Abelian Lie groups. Moreover there is usually some scaling or coupling parameter in the theory which in the limit relates to the classical theory. Fundamental topological aspects of such a quantum theory should be independent of the parameters and it is therefore reasonable to expect them to be computable (in some sense) by examining the classical limit. This means that such topological information is essentially robust and should be independent of the fine analytical details (and difficulties) of the full quantum theory. In the last decade much effort has been done to use these QFTs as a conceptual tool to suggest new mathematical results. In particular, they have led to spectacular progress in our understanding of geometry in low dimensions. It is most likely no accident that the usual QFTs can only be renormalized in (space–time) dimensions ≤4, and this is precisely the range in which difficult phenomena arise leading to deep and beautiful theories (e.g. the work of Thurston in three dimensions and Donaldson in four dimensions). It now seems clear that the way to investigate the subtleties of low-dimensional manifolds is to associate to them suitable infinite-dimensional manifolds (e.g. spaces of connections) and to study these by standard linear methods (homology, etc.). In other words we use QFT as a refined tool to study low-dimensional manifolds.
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BASEILHAC, P., and V. A. FATEEV. "FERMION–BOSON DUALITY IN INTEGRABLE QUANTUM FIELD THEORY." Modern Physics Letters A 13, no. 35 (November 20, 1998): 2807–18. http://dx.doi.org/10.1142/s0217732398002989.
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We introduce and study one-parameter family of integrable quantum field theories. This family has a Lagrangian description in terms of massive Thirring fermions ψ, ψ† and charged bosons χ, [Formula: see text] of complex sinh–Gordon model coupled with BCn affine Toda theory. Perturbative calculations, analysis of the factorized scattering theory and the Bethe ansatz technique are applied to show that under duality transformation, which relates weak and strong coupling regimes of the theory, the fermions ψ, ψ† transform to bosons and χ, [Formula: see text] and vice versa. The scattering amplitudes of neutral particles in this theory coincide exactly with S-matrix of particles in pure BCn Toda theory, i.e. the contribution of charged bosons and fermions to these amplitudes exactly cancel each other. We describe and discuss the symmetry responsible for this compensation property.