Journal articles: 'Symmetry (Physics) Group theory'

1

Villain, J. "Symmetry and group theory throughout physics." EPJ Web of Conferences 22 (2012): 00002. http://dx.doi.org/10.1051/epjconf/20122200002.

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Antoine, Jean-Pierre. "Group Theory: Mathematical Expression of Symmetry in Physics." Symmetry 13, no. 8 (July 26, 2021): 1354. http://dx.doi.org/10.3390/sym13081354.

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The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we first note that the basic principles imply that the state space of a quantum system has an intrinsic structure of pre-Hilbert space that one completes into a genuine Hilbert space. In this framework, the description of the invariance under a group G is based on a unitary representation of G. Next, we survey the various domains of application: atomic and molecular physics, quantum optics, signal and image processing, wavelets, internal symmetries, and approximate symmetries. Next, we discuss the extension to gauge theories, in particular, to the Standard Model of fundamental interactions. We conclude with some remarks about recent developments, including the application to braid groups.

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Ghaboussi, F. "Group theory of spontaneous symmetry breaking." International Journal of Theoretical Physics 26, no. 10 (October 1987): 957–66. http://dx.doi.org/10.1007/bf00670820.

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Green, HS. "A Cyclic Symmetry Principle in Physics." Australian Journal of Physics 47, no. 1 (1994): 25. http://dx.doi.org/10.1071/ph940025.

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Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow 7r-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow 7r-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras.

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Guo, Xiao Qiang, and Zheng Jun He. "The Applications of Group Theory." Advanced Materials Research 430-432 (January 2012): 1265–68. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.1265.

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Since the classification of finite simple groups completed last century, the applications of group theory are more and more widely. We first introduce the connection of groups and symmetry. And then we respectively introduce the applications of group theory in polynomial equation, algebraic topology, algebraic geometry , cryptography, algebraic number theory, physics and chemistry.

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Gu, Xiao-Yan, Fabien Gatti, Shi-Hai Dong, and Jian-Qiang Sun. "Symmetry and Group Theory and Its Application to Few-Body Physics." Advances in Mathematical Physics 2014 (2014): 1. http://dx.doi.org/10.1155/2014/486420.

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Lahoche, Vincent, and Dine Ousmane Samary. "Unitary symmetry constraints on tensorial group field theory renormalization group flow." Classical and Quantum Gravity 35, no. 19 (September 7, 2018): 195006. http://dx.doi.org/10.1088/1361-6382/aad83f.

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Kovalev, V. F., S. V. Krivenko, and V. V. Pustovalov. "Symmetry Group of Vlasov-Maxwell Equations in Plasma Theory." Journal of Nonlinear Mathematical Physics 3, no. 1-2 (January 1996): 175–80. http://dx.doi.org/10.2991/jnmp.1996.3.1-2.20.

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SHIRKOV, DMITRIJ V. "RENORMALIZATION GROUP SYMMETRY AND SOPHUS LIE GROUP ANALYSIS." International Journal of Modern Physics C 06, no. 04 (August 1995): 503–12. http://dx.doi.org/10.1142/s0129183195000356.

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We start with a short discussion of the content of a term Renormalisation Group in modern use. By treating the underlying solution property as a reparametrisation symmetry, we relate it with the self-similarity symmetry well-known in mathematical physics and explain the notion of Functional Self-similarity. Then we formulate a program of constructing a regular approach for discovering RG-type symmetries in different problems of mathematical physics. This approach based upon S. Lie group analysis allows one to analyse a wide class of boundary problems for different type of equations. Several examples are mentioned.

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Boyle, L. L. "The influence of abstract group theory on molecular symmetry." Journal of Physics: Conference Series 512 (May 12, 2014): 012019. http://dx.doi.org/10.1088/1742-6596/512/1/012019.

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GALAM, SERGE. "TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS." Modern Physics Letters B 01, no. 05n06 (August 1987): 239–44. http://dx.doi.org/10.1142/s0217984987000338.

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A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

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Guadagnini, E., M. Martellini, and M. Mintchev. "Braids and quantum group symmetry in Chern-Simons theory." Nuclear Physics B 336, no. 3 (June 1990): 581–609. http://dx.doi.org/10.1016/0550-3213(90)90443-h.

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Derkachov, S. E., and Y. M. Pis'mak. "Infinite symmetry group in D-dimensional conformal quantum field theory." Journal of Physics A: Mathematical and General 26, no. 6 (March 21, 1993): 1419–29. http://dx.doi.org/10.1088/0305-4470/26/6/023.

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BOHM, A., L. J. BOYA, P. KIELANOWSKI, M. KMIECIK, M. LOEWE, and P. MAGNOLLAY. "THEORY OF RELATIVISTIC EXTENDED OBJECTS." International Journal of Modern Physics A 03, no. 05 (May 1988): 1103–21. http://dx.doi.org/10.1142/s0217751x88000473.

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Physical ideas and mathematical methods of molecular and nuclear physics are extended into the relativistic domain. The resulting models are noncanonical modifications of restricted modes of the string. They describe collective motions of relativistic extended objects in terms of variables which are derived from the symmetry group (for the center-of-mass motion) and from the spectrum generating group (for the intrinsic motion). The simplest relativistic model of this kind is used to calculate spectrum and radiative transitions of hadrons.

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15

Wang, Zhenghan. "Beyond anyons." Modern Physics Letters A 33, no. 28 (September 11, 2018): 1830011. http://dx.doi.org/10.1142/s0217732318300112.

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The theory of anyon systems, as modular functors topologically and unitary modular tensor categories algebraically, is mature. To go beyond anyons, our first step is the interplay of anyons with conventional group symmetry due to the paramount importance of group symmetry in physics. This led to the theory of symmetry-enriched topological order. Another direction is the boundary physics of topological phases, both gapless as in the fractional quantum Hall physics and gapped as in the toric code. A more speculative and interesting direction is the study of Banados–Teitelboim–Zanelli (BTZ) black holes and quantum gravity in 3d. The clearly defined physical and mathematical issues require a far-reaching generalization of anyons and seem to be within reach. In this short survey, I will first cover the extensions of anyon theory to symmetry defects and gapped boundaries. Then, I will discuss a desired generalization of anyons to anyon-like objects — the BTZ black holes — in 3d quantum gravity.

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Hamadanian, Masood, and Ali Reza Ashrafi. "The full nonrigid group theory for trimethylamine." International Journal of Mathematics and Mathematical Sciences 2003, no. 42 (2003): 2701–6. http://dx.doi.org/10.1155/s0161171203205159.

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The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this note, a simple method is described by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of methyl groups attached to a rigid framework. We study the full NRG of trimethylamineN(CH3)3and prove that it is a group of order 1296 with 28 conjugacy classes. The method can be generalized to apply to other nonrigid molecules. The full nonrigid (f-NRG) molecule group theory is seen to be used advantageously to study the internal dynamics of such molecules.

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Gielen, Steffen. "Group Field Theory and Its Cosmology in a Matter Reference Frame." Universe 4, no. 10 (October 2, 2018): 103. http://dx.doi.org/10.3390/universe4100103.

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While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where coordinates are not a priori available and need to be reconstructed from physical degrees of freedom. We review the general idea of coupling free scalar fields to gravity and using these scalars as a “matter reference frame”. The resulting coordinate system is harmonic, i.e., it satisfies the harmonic (de Donder) gauge. We then show how to introduce such matter reference frames in the group field theory approach to quantum gravity, where spacetime is emergent from a “condensate” of fundamental quantum degrees of freedom of geometry, and how to use matter coordinates to extract physics. We review recent results in homogeneous and inhomogeneous cosmology, and give a new application to the case of spherical symmetry. We find tentative evidence that spherically-symmetric group field theory condensates defined in this setting can reproduce the near-horizon geometry of a Schwarzschild black hole.

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Moore, Gregory, and Nicolai Reshetikhin. "A comment on quantum group symmetry in conformal field theory." Nuclear Physics B 328, no. 3 (December 1989): 557–74. http://dx.doi.org/10.1016/0550-3213(89)90219-8.

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19

Ho, Choon-Lin. "Quantum group symmetry in multiple Chern - Simons theory on a torus." Journal of Physics A: Mathematical and General 29, no. 5 (March 7, 1996): L107—L113. http://dx.doi.org/10.1088/0305-4470/29/5/005.

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20

Itoh, Katsumi. "Gauge symmetry and the functional renormalization group." International Journal of Modern Physics A 32, no. 35 (December 20, 2017): 1747011. http://dx.doi.org/10.1142/s0217751x1747011x.

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In the functional renormalization group (FRG), the introduction of a momentum cutoff often breaks symmetry present in a theory. The most important example is the gauge symmetry. However a symmetry survives in the presence of a cutoff in a modified form. We apply our understanding to QED as the simplest case. A modified version of the Ward–Takahashi identity is solved partially to constrain the Wilson action. Furthermore, we study the flow equation for the photon 2-point function and find its analytical expression for the regulator function of the exponential type.

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Tovstyuk, K. D., C. C. Tovstyuk, and O. O. Danylevych. "The Permutation Group Theory and Electrons Interaction." International Journal of Modern Physics B 17, no. 21 (August 20, 2003): 3813–30. http://dx.doi.org/10.1142/s0217979203021812.

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The new mathematical formalism for the Green's functions of interacting electrons in crystals is constructed. It is based on the theory of Green's functions and permutation groups. We constructed a new object of permutation groups, which we call double permutation (DP). DP allows one to take into consideration the symmetry of the ground state as well as energy and momentum conservation in every virtual interaction. We developed the classification of double permutations and proved the theorem, which allows the selection of classes of associated double permutations (ADP). The Green's functions are constructed for series of ADP. We separate in the DP the convolving columns by replacing the initial interaction between the particles with the effective interaction. In convoluting the series for Green's functions, we use the methods developed for permutation groups schemes of Young–Yamanuti.

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22

LECLAIR, ANDRÉ, and F. A. SMIRNOV. "INFINITE QUANTUM GROUP SYMMETRY OF FIELDS IN MASSIVE 2D QUANTUM FIELD THEORY." International Journal of Modern Physics A 07, no. 13 (May 20, 1992): 2997–3022. http://dx.doi.org/10.1142/s0217751x92001332.

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Starting from a given S-matrix of an integrable quantum field theory in 1 + 1 dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by introducing an adjoint action of the symmetry generators on fields, and specifying the form factors of descendents. The braiding relations of quantum field multiplets is shown to be given by the universal ℛ-matrix. We develop in some detail the case of infinite-dimensional Yangian symmetry. We show that the quantum double of the Yangian is a Hopf algebra deformation of a level zero Kac–Moody algebra that preserves its finite-dimensional Lie subalgebra. The fields form infinite-dimensional Verma module representations; in particular, the energy–momentum tensor and isotopic current are in the same multiplet.

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FINKELSTEIN, R. J. "QUANTUM GROUPS AND FIELD THEORY." Modern Physics Letters A 15, no. 28 (September 14, 2000): 1709–15. http://dx.doi.org/10.1142/s0217732300002218.

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When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If the symmetry of a field theory is deformed in this way, the enlarged state space will again describe additional degrees of freedom, and the energy levels will acquire fine structure. The massive particles will have a stringlike spectrum lifting the degeneracy of the point-particle theory, and the resulting theory will have a nonlocal description. Theories of this kind naturally contain two sectors with one sector lying close to the standard theory while the second sector describes particles that should be more difficult to observe.

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KHVESHCHENKO, D. V., and P. B. WIEGMANN. "GAUGE THEORY OF ANTIFERROMAGNETISM IN TWO DIMENSIONS FOR LARGE RANK SYMMETRY GROUP." Modern Physics Letters B 04, no. 01 (January 10, 1990): 17–28. http://dx.doi.org/10.1142/s0217984990000040.

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We examine long wavelength fluctuations in two-dimensional magnetic systems with the symmetry group of a large rank N. The mean field solution is obtained and the existence of the parity-violating ground state is established. On the basis of the 1/N expansion, an effective gauge theory containing the Chern-Simons term is derived, which allows one to obtain a spectrum, spin and statistics of long wavelength excitations.

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Lev, Felix M. "Symmetries in Foundation of Quantum Theory and Mathematics." Symmetry 12, no. 3 (March 4, 2020): 409. http://dx.doi.org/10.3390/sym12030409.

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In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite—background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare symmetry can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario in which the phenomenon of cosmological acceleration can be explained by proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic p and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

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BANDELLONI, GIUSEPPE. "UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS." International Journal of Geometric Methods in Modern Physics 08, no. 03 (May 2011): 511–56. http://dx.doi.org/10.1142/s0219887811005269.

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The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

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SEREDYUK, B. A., K. D. TOVSTYUK, and N. K. TOVSTYUK. "APPLYING SYMMETRY PROPERTIES OF FINITE SYSTEM TO ITS FIELD THEORY DESCRIPTION." International Journal of Modern Physics B 18, no. 26 (October 30, 2004): 3443–50. http://dx.doi.org/10.1142/s0217979204026445.

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The self-energy is received using the theory group and field techniques, based on the wave functions of the classes of point symmetry group and accounting for the two-particle system. It contains components responsible not only for relaxation processes but also for the oscillating ones, caused by a different degree of occupation of the class of point symmetry group by particles of the structure. Analyzing the character of energy oscillations depending on the degree of the class occupation, the mechanisms of diffusion, catalysis, chemical reactions and Le-Shatelje principle are described.

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DUDEK, J., J. DOBACZEWSKI, N. DUBRAY, A. GÓŹDŹ, V. PANGON, and N. SCHUNCK. "NUCLEI WITH TETRAHEDRAL SYMMETRY." International Journal of Modern Physics E 16, no. 02 (February 2007): 516–32. http://dx.doi.org/10.1142/s0218301307005958.

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We discuss a point-group-theory based method of searching for new regions of nuclear stability. We illustrate the related strategy with realistic calculations employing the tetrahedral and the octahedral point groups. In particular, several nuclei in the Rare Earth region appear as excellent candidates to study the new mechanism.

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She, Zhen-Su, Xi Chen, and Fazle Hussain. "Quantifying wall turbulence via a symmetry approach: a Lie group theory." Journal of Fluid Mechanics 827 (August 22, 2017): 322–56. http://dx.doi.org/10.1017/jfm.2017.464.

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First-principle-based prediction of mean-flow quantities of wall-bounded turbulent flows (channel, pipe and turbulent boundary layer (TBL)) is of great importance from both physics and engineering standpoints. Here we present a symmetry-based approach which yields analytical expressions for the mean-velocity profile (MVP) from a Lie-group analysis. After verifying the dilatation-group invariance of the Reynolds averaged Navier–Stokes (RANS) equation in the presence of a wall, we depart from previous Lie-group studies of wall turbulence by selecting a stress length function as a similarity variable. We argue that this stress length function characterizes the symmetry property of wall flows having a simple dilatation-invariant form. Three kinds of (local) invariant forms of the length function are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall and hence also the MVP, using the mean-momentum equation. In particular, based on this multi-layer formula, we obtain analytical expressions for the (universal) wall function and separate wake functions for pipe and channel, which are validated by data from direct numerical simulations (DNS). In conclusion, an analytical expression for the entire MVP of wall turbulence, beyond the log law or power law, is developed in this paper and the theory can be used to describe the mean turbulent kinetic-energy distribution, as well as a variety of boundary conditions such as pressure gradient, wall roughness, buoyancy, etc. where the dilatation-group invariance is valid in the wall-normal direction.

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Shubashree, D., and R. Shankar. "Field Theory of Quantum Antiferromagnets: From the Triangular to the Kagome Lattice." International Journal of Modern Physics B 12, no. 07n08 (March 30, 1998): 781–802. http://dx.doi.org/10.1142/s0217979298000454.

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We analyse a family of models, that interpolates between the Triangular lattice antiferromagnet (TLAF) and the Kagome lattice antiferromagnet (KLAF). We identify the field theories governing the low energy, long wavelength physics of these models. Near the TLAF the low energy field theory is a nonlinear sigma model of a SO(3) group valued field. The SO(3) symmetry of the spin system is enhanced to a SO(3)R × SO(2)L symmetry in the field theory. Near the KLAF other modes become important and the field takes values in SO(3) × S2 . We analyse this field theory and show that it admits a novel phase in which the SO(3)R spin symmetry is unbroken and the SO(2)L symmetry is broken. We propose this as a possible mechanism by which a gapless excitation can exist in the KLAF without breaking the spin rotation symmetry.

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LÜST, DIETER, and STEFAN THEISEN. "EXCEPTIONAL GROUPS IN STRING THEORY." International Journal of Modern Physics A 04, no. 17 (October 20, 1989): 4513–33. http://dx.doi.org/10.1142/s0217751x89001916.

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We review the occurrence of exceptional groups in string theory: their dual role as gauge symmetry and as a symmetry unifying space-time, superconformal ghost and internal degrees of freedom. In both cases the relation to the extended world-sheet supersymmetries is discussed in detail. This is used to construct the supermultiplet structure of the massless sectors of all supergravity theories possible in string theory, in even space-time dimensions between four and ten.

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Dotsenko, V., and D. E. Feldman. "Replica symmetry breaking and the renormalization group theory of the weakly disordered ferromagnet." Journal of Physics A: Mathematical and General 28, no. 18 (September 21, 1995): 5183–206. http://dx.doi.org/10.1088/0305-4470/28/18/010.

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Brody, Dorje C., and Lane P. Hughston. "Theory of quantum space-time." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2061 (July 25, 2005): 2679–99. http://dx.doi.org/10.1098/rspa.2005.1457.

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A generalized equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking . Based on this principle, a higher-dimensional extension of Minkowski space is proposed and its properties examined. In this scheme the structure of space-time is intrinsically quantum mechanical. It is shown that the causal geometry of such a quantum space-time (QST) possesses a rich hierarchical structure. The natural extension of the Poincaré group to QST is investigated. In particular, we prove that the symmetry group of this space is generated in general by a system of irreducible Killing tensors. After the symmetries are broken, the points of the QST can be interpreted as space-time valued operators . The generic point of a QST in the broken symmetry phase then becomes a Minkowski space-time valued operator. Classical space-time emerges as a map from QST to Minkowski space. It is shown that the general such map satisfying appropriate causality-preserving conditions ensuring linearity and Poincaré invariance is necessarily a density matrix.

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GAO, YA-JUN. "NEW INFINITE-DIMENSIONAL DOUBLE SYMMETRY GROUPS FOR THE EINSTEIN–KALB–RAMOND THEORY." International Journal of Modern Physics A 23, no. 10 (April 20, 2008): 1593–612. http://dx.doi.org/10.1142/s0217751x08039694.

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The symmetry structures of the dimensionally reduced Einstein–Kalb–Ramond (EKR) theory is further studied. By using a so-called extended double (ED)-complex method, the usual Riemann–Hilbert (RH) problem is extended to an ED-complex formulation. A pair of ED RH transformations are constructed and they are verified to give infinite-dimensional double symmetry groups of the EKR theory, each of these symmetry groups has the structure of semidirect product of Kac–Moody group [Formula: see text] and Virasoro group. Moreover, the infinitesimal forms of these RH transformations are calculated out and they are found to give exactly the same results as previous, these demonstrate that the pair of ED RH transformations in this paper provide exponentiations of all the infinitesimal symmetries in our previous paper. The finite forms of symmetry transformations given in the present paper are more important and useful for theoretic studies and new solution generation, etc.

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Basso, E., and Daniel J. H. Chung. "Lorentz invariance of basis tensor gauge theory." International Journal of Modern Physics A 36, no. 17 (June 7, 2021): 2150099. http://dx.doi.org/10.1142/s0217751x21500998.

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Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an [Formula: see text] permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.

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AHN, CHANGHYUN. "META-STABLE BRANE CONFIGURATION AND GAUGED FLAVOR SYMMETRY." Modern Physics Letters A 22, no. 31 (October 10, 2007): 2329–41. http://dx.doi.org/10.1142/s0217732307024346.

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Starting from an [Formula: see text] supersymmetric electric gauge theory with the gauge group Sp (N c ) × SO (2N′ c ) with fundamentals for the first gauge group factor and a bifundamental, we apply Seiberg dual to the symplectic gauge group only and arrive at the [Formula: see text] supersymmetric dual magnetic gauge theory with dual matters including the gauge singlets and superpotential. By analyzing the F-term equations of the dual magnetic superpotential, we describe the intersecting brane configuration of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory.

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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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RASMUSSEN, JØRGEN. "THREE-POINT FUNCTIONS IN CONFORMAL FIELD THEORY WITH AFFINE LIE GROUP SYMMETRY." International Journal of Modern Physics A 14, no. 08 (March 30, 1999): 1225–59. http://dx.doi.org/10.1142/s0217751x99000634.

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In this paper we develop a general method for constructing three-point functions in conformal field theory with affine Lie group symmetry, continuing our recent work on two-point functions. The results are provided in terms of triangular coordinates used in a wave function description of vectors in highest weight modules. In this framework, complicated couplings translate into ordinary products of certain elementary polynomials. The discussions pertain to all simple Lie groups and arbitrary integrable representation. An interesting by-product is a general procedure for computing tensor product coefficients, essentially by counting integer solutions to certain inequalities. As an illustration of the construction, we consider in great detail the three cases SL(3), SL(4) and SO(5).

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CHAO, LIU, and BO-YU HOU. "BOSONIC SUPERCONFORMAL AFFINE TODA THEORY: EXCHANGE ALGEBRA AND DRESSING SYMMETRY." International Journal of Modern Physics A 08, no. 21 (August 20, 1993): 3773–89. http://dx.doi.org/10.1142/s0217751x93001533.

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We propose and investigate a new conformal invariant integrable field theory called bosonic superconformal affine Toda theory. This theory can be viewed either as the affine generalization of the so-called bosonic superconformal Toda theory studied by the authors sometime earlier, or as the generalization to the case of half-integer conformal weights of the conformal affine Toda theory, and can also be obtained from the Hamiltonian reduction of WZNW theory (with an affine WZNW group). The fundamental Poisson stracture is established in terms of the classical r matrix. Then the exchange algebra for the chiral vectors is obtained as well as the reconstruction formula for the classical solutions. The dressing transformations of the fundamental fields are found explicitly, and the Poisson-Lie structure of the dressing group is also constructed with the aid of classical exchange algebras, which turns out to be the semiclassical limit of the quantum affine group. The conformal breaking orbit of the model is also studied, which is called bosonic super loop Toda theory in the context. In addition, the quantum exchange relation and quantum group symmetry are discussed briefly.

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40

Zingoni, Alphose. "Group-theoretic insights on the vibration of symmetric structures in engineering." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2008 (February 13, 2014): 20120037. http://dx.doi.org/10.1098/rsta.2012.0037.

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Group theory has been used to study various problems in physics and chemistry for many years. Relatively recently, applications have emerged in engineering, where problems of the vibration, bifurcation and stability of systems exhibiting symmetry have been studied. From an engineering perspective, the main attraction of group-theoretic methods has been their potential to reduce computational effort in the analysis of large-scale problems. In this paper, we focus on vibration problems in structural mechanics and reveal some of the insights and qualitative benefits that group theory affords. These include an appreciation of all the possible symmetries of modes of vibration, the prediction of the number of modes of a given symmetry type, the identification of modes associated with the same frequencies, the prediction of nodal lines and stationary points of a vibrating system, and the untangling of clustered frequencies.

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Aksoy, Yiğit, Tasawar Hayat, and Mehmet Pakdemirli. "Boundary Layer Theory and Symmetry Analysis of a Williamson Fluid." Zeitschrift für Naturforschung A 67, no. 6-7 (July 1, 2012): 363–68. http://dx.doi.org/10.5560/zna.2012-0028.

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Boundary layer equations are derived for the first time for a Williamson fluid. Using Lie group theory, a symmetry analysis of the equations is performed. The partial differential system is transferred to an ordinary differential system via symmetries, and the resulting equations are numerically solved. Finally, the effects of the non-Newtonian parameters on the solutions are discussed

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ALDAYA, V., M. CALIXTO, J. GUERRERO, and F. F. LÓPEZ-RUIZ. "SYMMETRIES OF NON-LINEAR SYSTEMS: GROUP APPROACH TO THEIR QUANTIZATION." International Journal of Geometric Methods in Modern Physics 08, no. 06 (September 2011): 1329–54. http://dx.doi.org/10.1142/s0219887811005713.

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We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically non-perturbative, is primarily intended for non-linear systems, although needless to say that finding the basic symmetry associated with a given (quantum) physical problem is in general a difficult task, which many times nearly emulates the complexity of finding the actual (classical) solutions. Apart from some interesting examples related to the electromagnetic and gravitational particle interactions, where an algebraic version of the Equivalence Principle naturally arises, we attempt to the quantum description of non-linear sigma models. In particular, we present the actual quantization of the partial-trace non-linear SU (2) sigma model as a representative case of non-linear quantum field theory.

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JULVE, J., and A. TIEMBLO. "DYNAMICAL VARIABLES IN GAUGE-TRANSLATIONAL GRAVITY." International Journal of Geometric Methods in Modern Physics 08, no. 02 (March 2011): 381–93. http://dx.doi.org/10.1142/s0219887811005191.

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Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first principles we verify that a nonlinear realization of the symmetry provides the general structure of this gauge theory, leading to a simple choice of dynamical variables of the gravity field corresponding, at first-order, to a diagonal matrix, whereas the non-diagonal elements contribute only to higher orders.

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Guo, Xiao-Kan. "Thermofield double states in group field theory." International Journal of Modern Physics A 36, no. 02 (January 20, 2021): 2150008. http://dx.doi.org/10.1142/s0217751x21500081.

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Group field theories are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermofield double states in group field theories. The starting point is the equilibrium Gibbs states in group field theory recently found by Kotecha and Oriti, based on which we construct the thermofield double state as a “thermal” vacuum respecting the Kubo–Martin–Schwinger condition. We work with the Weyl [Formula: see text]-algebra of group fields, and a particular type of thermofield double states with single type of symmetry is obtained from the squeezed states on this Weyl algebra. The thermofield double states, when viewed as states on the group field theory Fock vacuum, are condensate states at finite flow parameter [Formula: see text]. We suggest that the equilibrium flow parameters [Formula: see text] of this type of thermofield double states in the group field theory condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.

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CRANE, LOUIS. "STRING FIELD THEORY FROM QUANTUM GRAVITY." Reviews in Mathematical Physics 25, no. 10 (November 2013): 1343005. http://dx.doi.org/10.1142/s0129055x13430058.

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Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) representations is just the dual model on the extended lattice of the Lie group E6, as explained by the quantum McKay correspondence of Frenkel, Jing and Wang. The coupled model can be thought of as string field theory, but propagating on a discretized quantum spacetime rather than a classical manifold.

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Abila, Agatha Kristel, Ma Louise Antonette De Las Peñas, and Eduard Taganap. "Local and global color symmetries of a symmetrical pattern." Acta Crystallographica Section A Foundations and Advances 75, no. 5 (August 23, 2019): 730–45. http://dx.doi.org/10.1107/s2053273319008763.

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This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.

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Friedman, Yaakov, and Tzvi Scarr. "Symmetry and Special Relativity." Symmetry 11, no. 10 (October 3, 2019): 1235. http://dx.doi.org/10.3390/sym11101235.

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We explore the role of symmetry in the theory of Special Relativity. Using the symmetry of the principle of relativity and eliminating the Galilean transformations, we obtain a universally preserved speed and an invariant metric, without assuming the constancy of the speed of light. We also obtain the spacetime transformations between inertial frames depending on this speed. From experimental evidence, this universally preserved speed is c, the speed of light, and the transformations are the usual Lorentz transformations. The ball of relativistically admissible velocities is a bounded symmetric domain with respect to the group of affine automorphisms. The generators of velocity addition lead to a relativistic dynamics equation. To obtain explicit solutions for the important case of the motion of a charged particle in constant, uniform, and perpendicular electric and magnetic fields, one can take advantage of an additional symmetry—the symmetric velocities. The corresponding bounded domain is symmetric with respect to the conformal maps. This leads to explicit analytic solutions for the motion of the charged particle.

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GAETA, GIUSEPPE. "BREAKING OF LINEAR SYMMETRIES AND MICHEL'S THEORY: GRASSMANN MANIFOLDS, AND INVARIANT SUBSPACES." International Journal of Modern Physics A 23, no. 03n04 (February 10, 2008): 547–65. http://dx.doi.org/10.1142/s0217751x08038639.

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Michel's theory of symmetry breaking in its original formulation has some difficulty in dealing with problems with a linear symmetry, due to the degeneration in the symmetry type implied by the linearity of group action. Here we propose a fully geometric, approach to the problem, making use of Grassmann manifolds. In this way Michel theory can also be applied to the determination of dynamically invariant manifolds for equivariant nonlinear flows.

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COTĂESCU, ION I. "COVARIANT REPRESENTATIONS OF THE DE SITTER ISOMETRY GROUP." Modern Physics Letters A 28, no. 09 (March 21, 2013): 1350033. http://dx.doi.org/10.1142/s0217732313500338.

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We show that the induced representations of the de Sitter isometry group proposed many years ago by Nachtmann are equivalent to those derived from our general theory of external symmetry. These methods complete each other leading to a coherent theory of covariant fields with spin on the de Sitter spacetime. Some technical details of these representations are presented here for the first time.

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Kramer, P. "On the Theory of a Non-Periodic Quasilattice Associated with the Icosahedral Group." Zeitschrift für Naturforschung A 40, no. 8 (August 1, 1985): 775–88. http://dx.doi.org/10.1515/zna-1985-0801.

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A quasilattice in the euclidean space E3 is generated by dualization of a hexagrid. The construction is based on a general theory of periodic and non-periodic space filling by projection from hypergrids. Global and local properties of the quasilattice are discussed, including the structure factor, the form and packing of the cells, and the point symmetry. The quasilattice is expected to give a description of quasicrystals without periodic order which have recently been found in experiments.

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Journal articles on the topic 'Symmetry (Physics) Group theory'

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