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Journal articles on the topic '1-dimensional symmetry'

Author: Grafiati

Published: 9 March 2023

Last updated: 19 July 2025

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1

Konopelchenko, Boris, Jurij Sidorenko, and Walter Strampp. "(1+1)-dimensional integrable systems as symmetry constraints of (2+1)-dimensional systems." Physics Letters A 157, no. 1 (1991): 17–21. http://dx.doi.org/10.1016/0375-9601(91)90402-t.

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2

Khalil, S. S. "«Chiral» symmetry in (2+1)-dimensional QCD." Il Nuovo Cimento A 107, no. 5 (1994): 689–96. http://dx.doi.org/10.1007/bf02732078.

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3

KOVNER, A., and B. ROSENSTEIN. "MASSLESSNESS OF PHOTON AND CHERN-SIMONS TERM IN (2 + 1)-DIMENSIONAL QED." Modern Physics Letters A 05, no. 31 (1990): 2661–68. http://dx.doi.org/10.1142/s0217732390003103.

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We study the realization of global symmetries in (2 + 1)-dimensional QED with two fermion flavors. It is shown that, in a certain range of mass parameters, the chiral symmetry [Formula: see text] and the flux symmetry Φ = ∫d2xB are both spontaneously broken, but the combination I = Q5 − sign (m)e/πΦ remains unbroken. The photon is identified with the corresponding massless excitation, which is required in this case by Goldstone theorem. An order parameter vanishes and chiral and flux symmetries are realized in the Kosterlitz-Thouless mode. Outside this range of parameters the vacuum is symmetric and simultaneously the photon's topological mass is generated. Similar symmetry breaking pattern U (1) ⊗ U (1) → U (1) is realized in Chern-Simons electrodynamics for a particular value of the bare CS-term coefficient at which the "statistical photon" becomes massless. We point out the direct correspondence of this model to the superconducting anyon gas.

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4

Hu, Hengchun, and Xiaodan Li. "Nonlocal symmetry and interaction solutions for the new (3+1)-dimensional integrable Boussinesq equation." Mathematical Modelling of Natural Phenomena 17 (2022): 2. http://dx.doi.org/10.1051/mmnp/2022001.

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The nonlocal symmetry of the new (3+1)-dimensional Boussinesq equation is obtained with the truncated Painlevé method. The nonlocal symmetry can be localized to the Lie point symmetry for the prolonged system by introducing auxiliary dependent variables. The finite symmetry transformation related to the nonlocal symmetry of the integrable (3+1)-dimensional Boussinesq equation is studied. Meanwhile, the new (3+1)-dimensional Boussinesq equation is proved by the consistent tanh expansion method and many interaction solutions among solitons and other types of nonlinear excitations such as cnoidal periodic waves and resonant soliton solution are given.

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5

Yang, Huizhang, Wei Liu, and Yunmei Zhao. "Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation." Complexity 2020 (October 24, 2020): 1–8. http://dx.doi.org/10.1155/2020/3465860.

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In this paper, the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP) equation is studied applying Lie symmetry analysis. We apply the Lie symmetry method to the (3 + 1)-dimensional generalized BKP equation and derive its symmetry reductions. Based on these symmetry reductions, some exact traveling wave solutions are obtained by using the tanh method and Kudryashov method. Finally, the conservation laws to the (3 + 1)-dimensional generalized BKP equation are presented by invoking the multiplier method.

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6

ARIK, METIN, and MUHITTIN MUNGAN. "SYMMETRY CHANGES DURING THE EVOLUTION OF THE UNIVERSE." Modern Physics Letters A 05, no. 31 (1990): 2593–98. http://dx.doi.org/10.1142/s0217732390003012.

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This article investigates a (2 + 1)-dimensional universe evolving from a spherically symmetric spatial structure into the Kaluza-Klein structure. The implications of the symmetry change are discussed for this model in particular and also in general. It turns out that for such symmetry changes, the energy density is ill-defined for early times.

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7

Maris, Pieter, and Dean Lee. "Chiral symmetry breaking in (2+1) dimensional QED." Nuclear Physics B - Proceedings Supplements 119 (May 2003): 784–86. http://dx.doi.org/10.1016/s0920-5632(03)80467-x.

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8

Babu, K. S., P. Panigrahi, and S. Ramaswamy. "Radiative symmetry breaking in (2+1)-dimensional space." Physical Review D 39, no. 4 (1989): 1190–95. http://dx.doi.org/10.1103/physrevd.39.1190.

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9

Oshima, Kazuto. "Spontaneous Symmetry Breaking in (1+1)-Dimensional Light-Front φ4Theory". Journal of the Physical Society of Japan 72, № 1 (2003): 83–88. http://dx.doi.org/10.1143/jpsj.72.83.

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10

Luo, Xiang-Qian. "Chiral-Symmetry Breaking in (1+1)-Dimensional Lattice Gauge Theories." Communications in Theoretical Physics 16, no. 4 (1991): 505–8. http://dx.doi.org/10.1088/0253-6102/16/4/505.

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11

LIN JI, YU JUN, and LOU SEN-YUE. "(3+1)-DIMENSIONAL MODELS WITH INFINITELY DIMENSIONAL VIRASORO TYPE SYMMETRY ALGBRA." Acta Physica Sinica 45, no. 7 (1996): 1073. http://dx.doi.org/10.7498/aps.45.1073.

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12

SINHA, A., and P. ROY. "(1+1)-DIMENSIONAL DIRAC EQUATION WITH NON-HERMITIAN INTERACTION." Modern Physics Letters A 20, no. 31 (2005): 2377–85. http://dx.doi.org/10.1142/s0217732305017664.

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We study (1+1)-dimensional Dirac equation with non-Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo-supersymmetry.

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13

BLACKBURN, H. M., and J. M. LOPEZ. "Modulated waves in a periodically driven annular cavity." Journal of Fluid Mechanics 667 (November 25, 2010): 336–57. http://dx.doi.org/10.1017/s0022112010004520.

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Time-periodic flows with spatio-temporal symmetry Z2 × O(2) – invariance in the spanwise direction generating the O(2) symmetry group and a half-period-reflection symmetry in the streamwise direction generating a spatio-temporal Z2 symmetry group – are of interest largely because this is the symmetry group of periodic laminar two-dimensional wakes of symmetric bodies. Such flows are the base states for various three-dimensional instabilities; the periodically shedding two-dimensional circular cylinder wake with three-dimensional modes A and B being the generic example. However, it is not easy to physically realize the ideal flows owing to the presence of end effects and finite spanwise geometries. Flows past rings are sometimes advanced as providing a relevant idealization, but in fact these have symmetry group O(2) and only approach Z2 × O(2) symmetry in the infinite aspect ratio limit. The present work examines physically realizable periodically driven annular cavity flows that possess Z2 × O(2) spatio-temporal symmetry. The flows have three distinct codimension-1 instabilities: two synchronous modes (A and B), and two manifestations of a quasi-periodic (QP) mode, either as modulated standing waves or modulated travelling waves. It is found that the curvature of the system can determine which of these modes is the first to become unstable with increasing Reynolds number, and that even in the nonlinear regime near onset of three-dimensional instabilities the dynamics are dominated by mixed modes with complicated spatio-temporal structure. Supplementary movies illustrating the spatio-temporal dynamics are available at journals.cambridge.org/flm.

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14

Kotikov, Anatoly V., and Sofian Teber. "Critical Behavior of (2 + 1)-Dimensional QED: 1/N Expansion." Particles 3, no. 2 (2020): 345–54. http://dx.doi.org/10.3390/particles3020026.

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We present recent results on dynamical chiral symmetry breaking in (2 + 1)-dimensional QED with N four-component fermions. The results of the 1 / N expansion in the leading and next-to-leading orders were found exactly in an arbitrary nonlocal gauge.

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15

Tobita, Yutaka, and Jun Goryo. "Tobological feedback for superconducting states." Journal of Physics: Conference Series 2164, no. 1 (2022): 012010. http://dx.doi.org/10.1088/1742-6596/2164/1/012010.

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Abstract We discuss feedback effects that stabilize the superconducting states by the induced topological term in the effective Lagrangian. The chiral feedback effect due to the Chern-Simons-like term for quasi-two-dimensional system with time-reversal symmetry breaking (TRSB) was studied in [1, 2]. We consider the extension of the chiral feedback to three-dimensional TRSB system and investigate similar feedback effects for quasi-two-dimensional or three-dimensional time-reversal symmetric systems.

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16

WU, YUE-LIANG. "MAXIMALLY SYMMETRIC MINIMAL UNIFICATION MODEL SO(32) WITH THREE FAMILIES IN TEN-DIMENSIONAL SPACETIME." Modern Physics Letters A 22, no. 04 (2007): 259–71. http://dx.doi.org/10.1142/s0217732307022591.

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Based on a maximally symmetric minimal unification hypothesis and a quantum charge-dimension correspondence principle, it is demonstrated that each family of quarks and leptons belongs to the Majorana–Weyl spinor representation of 14 dimensions that relate to quantum spin-isospin-color charges. Families of quarks and leptons attribute to a spinor structure of extra six dimensions that relate to quantum family charges. Of particular, it is shown that ten dimensions relating to quantum spin-family charges form a motional ten-dimensional quantum spacetime with a generalized Lorentz symmetry SO (1, 9), and ten dimensions relating to quantum isospin-color charges become a motionless ten-dimensional quantum intrinsic space. Its corresponding 32-component fermions in the spinor representation possess a maximal gauge symmetry SO (32). As a consequence, a maximally symmetric minimal unification model SO (32) containing three families in ten-dimensional quantum spacetime is naturally obtained by choosing a suitable Majorana–Weyl spinor structure into which quarks and leptons are directly embedded. Both resulting symmetry and dimensions coincide with those of type I string and heterotic string SO (32) in string theory.

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17

HALL, BRIAN C. "COHERENT STATES AND THE QUANTIZATION OF (1+1)-DIMENSIONAL YANG–MILLS THEORY." Reviews in Mathematical Physics 13, no. 10 (2001): 1281–305. http://dx.doi.org/10.1142/s0129055x0100096x.

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This paper discusses the canonical quantization of (1+1)-dimensional Yang–Mills theory on a spacetime cylinder from the point of view of coherent states, or equivalently, the Segal–Bargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinite-dimensional linear phase space. Gauge symmetry is imposed by projecting the original coherent states onto the gauge-invariant subspace, using a suitable regularization procedure. We obtain in this way a new family of "reduced" coherent states labeled by points in the reduced phase space, which in this case is simply the cotangent bundle of the structure group K. The main result explained here, obtained originally in a joint work of the author with B. Driver, is this: The reduced coherent states are precisely those associated to the generalized Segal–Bargmann transform for K, as introduced by the author from a different point of view. This result agrees with that of K. Wren, who uses a different method of implementing the gauge symmetry. The coherent states also provide a rigorous way of making sense out of the quantum Hamiltonian for the unreduced system. Various related issues are discussed, including the complex structure on the reduced phase space and the question of whether quantization commutes with reduction.

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18

Thiam, Lamine, and Xi-zhong Liu. "Residual Symmetry Reduction and Consistent Riccati Expansion to a Nonlinear Evolution Equation." Complexity 2019 (November 13, 2019): 1–9. http://dx.doi.org/10.1155/2019/6503564.

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The residual symmetry of a (1 + 1)-dimensional nonlinear evolution equation (NLEE) ut+uxxx−6u2ux+6λux=0 is obtained through Painlevé expansion. By introducing a new dependent variable, the residual symmetry is localized into Lie point symmetry in an enlarged system, and the related symmetry reduction solutions are obtained using the standard Lie symmetry method. Furthermore, the (1 + 1)-dimensional NLEE equation is proved to be integrable in the sense of having a consistent Riccati expansion (CRE), and some new Bäcklund transformations (BTs) are given. In addition, some explicitly expressed solutions including interaction solutions between soliton and cnoidal waves are derived from these BTs.

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19

Jarmolińska, Sylwia, Agnieszka Feliczak-Guzik, and Izabela Nowak. "Synthesis, Characterization and Use of Mesoporous Silicas of the Following Types SBA-1, SBA-2, HMM-1 and HMM-2." Materials 13, no. 19 (2020): 4385. http://dx.doi.org/10.3390/ma13194385.

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Mesoporous silicas have enjoyed great interest among scientists practically from the moment of their discovery thanks to their unique attractive properties. Many types of mesoporous silicas have been described in literature, the most thoroughly MCM-41 and SBA-15 ones. The focus of this review are the methods of syntheses, characterization and use of mesoporous silicas from SBA (Santa Barbara Amorphous) and HMM (Hybrid Mesoporous Materials) groups. The first group is represented by (i) SBA-1 of three-dimensional cubic structure and Pm3¯n symmetry and (ii) SBA-2 of three-dimensional combined hexagonal and cubic structures and P63/mmc symmetry. The HMM group is represented by (i) HMM-1 of two-dimensional hexagonal structure and p6mm symmetry and (ii) HMM-2 of three-dimensional structure and P63/mmc symmetry. The paper provides comprehensive information on the above-mentioned silica materials available so far, also including the data for the silicas modified with metal ions or/and organic functional groups and examples of the materials applications.

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20

Chiang, Cheng-Wei, Takaaki Nomura, and Joe Sato. "Gauge-Higgs Unification Models in Six Dimensions withS2/Z2Extra Space and GUT Gauge Symmetry." Advances in High Energy Physics 2012 (2012): 1–39. http://dx.doi.org/10.1155/2012/260848.

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We review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime withS2/Z2topology in the extra spatial dimensions. Nontrivial boundary conditions are imposed on the extraS2/Z2space. This review considers two scenarios for constructing a four-dimensional theory from the six-dimensional model. One scheme utilizes the SO(12) gauge symmetry with a special symmetry condition imposed on the gauge field, whereas the other employs the E6gauge symmetry without requiring the additional symmetry condition. Both models lead to a standard model-like gauge theory with theSU(3)×SU(2)L×U(1)Y(×U(1)2)symmetry and SM fermions in four dimensions. The Higgs sector of the model is also analyzed. The electroweak symmetry breaking can be realized, and the weak gauge boson and Higgs boson masses are obtained.

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21

Wang, Haifeng, and Yufeng Zhang. "Residual Symmetries and Bäcklund Transformations of (2 + 1)-Dimensional Strongly Coupled Burgers System." Advances in Mathematical Physics 2020 (January 23, 2020): 1–8. http://dx.doi.org/10.1155/2020/6821690.

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In this article, we mainly apply the nonlocal residual symmetry analysis to a (2 + 1)-dimensional strongly coupled Burgers system, which is defined by us through taking values in a commutative subalgebra. On the basis of the general theory of Painlevé analysis, we get a residual symmetry of the strongly coupled Burgers system. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a Bäcklund transformation is derived by Lie’s first theorem. Further, the linear superposition of the multiple residual symmetries is localized to a Lie point symmetry, and an N-th Bäcklund transformation is also obtained.

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22

Lin, Ji. "(3+1)-Dimensional Integrable Models Possessing Infinite Dimensional Virasoro-Type Symmetry Algebra." Communications in Theoretical Physics 25, no. 4 (1996): 447–50. http://dx.doi.org/10.1088/0253-6102/25/4/447.

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23

Lou, Sen-yue, Ji Lin, and Jun Yu. "(3 + 1)-dimensional models with an infinitely dimensional Virasoro type symmetry algebra." Physics Letters A 201, no. 1 (1995): 47–52. http://dx.doi.org/10.1016/0375-9601(95)00201-d.

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24

Hu, Xiao-Rui, and Yong Chen. "Two-dimensional symmetry reduction of (2+1)-dimensional nonlinear Klein–Gordon equation." Applied Mathematics and Computation 215, no. 3 (2009): 1141–45. http://dx.doi.org/10.1016/j.amc.2009.06.049.

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25

Wang, Gangwei, Yixing Liu, Shuxin Han, Hua Wang, and Xing Su. "Generalized Symmetries and mCK Method Analysis of the (2+1)-Dimensional Coupled Burgers Equations." Symmetry 11, no. 12 (2019): 1473. http://dx.doi.org/10.3390/sym11121473.

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In this paper, generalized symmetries and mCK method are employed to analyze the (2+1)-dimensional coupled Burgers equations. Firstly, based on the generalized symmetries method, the corresponding symmetries of the (2+1)-dimensional coupled Burgers equations are derived. And then, using the mCK method, symmetry transformation group theorem is presented. From symmetry transformation group theorem, a great many of new solutions can be derived. Lastly, Lie algebra for given symmetry group are considered.

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26

Jadaun, Vishakha, and Sachin Kumar. "Symmetry analysis and invariant solutions of (3 + 1)-dimensional Kadomtsev–Petviashvili equation." International Journal of Geometric Methods in Modern Physics 15, no. 08 (2018): 1850125. http://dx.doi.org/10.1142/s0219887818501256.

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Based on Lie symmetry analysis, we study nonlinear waves in fluid mechanics with strong spatial dispersion. The similarity reductions and exact solutions are obtained based on the optimal system and power series method. We obtain the infinitesimal generators, commutator table of Lie algebra, symmetry group and similarity reductions for the [Formula: see text]-dimensional Kadomtsev–Petviashvili equation. For different Lie algebra, Lie symmetry method reduces Kadomtsev–Petviashvili equation into various ordinary differential equations (ODEs). Some of the solutions of [Formula: see text]-dimensional Kadomtsev–Petviashvili equation are of the forms — traveling waves, Weierstrass’s elliptic and Zeta functions and exponential functions.

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27

Hua, Xiaorui, Zhongzhou Dongb, Fei Huangc, and Yong Chena. "Symmetry Reductions and Exact Solutions of the (2+1)-Dimensional Navier-Stokes Equations." Zeitschrift für Naturforschung A 65, no. 6-7 (2010): 504–10. http://dx.doi.org/10.1515/zna-2010-6-704.

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By means of the classical symmetry method, we investigate the (2+1)-dimensional Navier-Stokes equations. The symmetry group of Navier-Stokes equations is studied and its corresponding group invariant solutions are constructed. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, using the associated vector fields of the obtained symmetry, we give out the reductions by one-dimensional and two-dimensional subalgebras, and some explicit solutions of Navier-Stokes equations are obtained. For three interesting solutions, the figures are given out to show their properties: the solution of stationary wave of fluid (real part) appears as a balance between fluid advection (nonlinear term) and friction parameterized as a horizontal harmonic diffusion of momentum.

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28

Qu, Chang-Zheng. "Symmetry Algebras of Generalized (2 + 1)-Dimensional KdV Equation." Communications in Theoretical Physics 25, no. 3 (1996): 369–72. http://dx.doi.org/10.1088/0253-6102/25/3/369.

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29

Polychronakos, Alexios P. "Symmetry-Breaking Patterns in (2+1)-Dimensional Gauge Theories." Physical Review Letters 60, no. 19 (1988): 1920–23. http://dx.doi.org/10.1103/physrevlett.60.1920.

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30

Zhao, Jing. "SYMMETRY ANALYSIS OF THE 2 + 1 DIMENSIONAL DIFFUSION EQUATION." Far East Journal of Applied Mathematics 94, no. 1 (2016): 55–62. http://dx.doi.org/10.17654/am094010055.

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31

Lou, Sen-Yue, Jun Yu, and Ji Lin. "(2+1)-dimensional models with Virasoro-type symmetry algebra." Journal of Physics A: Mathematical and General 28, no. 6 (1995): L191—L196. http://dx.doi.org/10.1088/0305-4470/28/6/002.

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32

Ruo-Xia, Yao, and Lou Sen-Yue. "A Maple Package to Compute Lie Symmetry Groups and Symmetry Reductions of (1+1)-Dimensional Nonlinear Systems." Chinese Physics Letters 25, no. 6 (2008): 1927–30. http://dx.doi.org/10.1088/0256-307x/25/6/002.

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33

HAYASHI, MASAKO, and TOMOHIRO INAGAKI. "CURVATURE AND TOPOLOGICAL EFFECTS ON DYNAMICAL SYMMETRY BREAKING IN A FOUR- AND EIGHT-FERMION INTERACTION MODEL." International Journal of Modern Physics A 25, no. 17 (2010): 3353–74. http://dx.doi.org/10.1142/s0217751x10049426.

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A dynamical mechanism for symmetry breaking is investigated under the circumstances with the finite curvature, finite size and nontrivial topology. A four- and eight-fermion interaction model is considered as a prototype model which induces symmetry breaking at GUT era. Evaluating the effective potential in the leading order of the 1/N-expansion by using the dimensional regularization, we explicitly calculate the phase boundary which divides the symmetric and the broken phase in a weakly curved space–time and a flat space–time with nontrivial topology, RD-1 ⊗ S1.

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34

Cheng, Wenguang, and Biao Li. "Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation." Zeitschrift für Naturforschung A 71, no. 4 (2016): 351–56. http://dx.doi.org/10.1515/zna-2015-0504.

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AbstractThe truncated Painlevé method is developed to obtain the nonlocal residual symmetry and the Bäcklund transformation for the (2+1)-dimensional KdV–mKdV equation. The residual symmetry is localised after embedding the (2+1)-dimensional KdV–mKdV equation to an enlarged one. The symmetry group transformation of the enlarged system is computed. Furthermore, the (2+1)-dimensional KdV–mKdV equation is proved to be consistent Riccati expansion (CRE) solvable. The soliton–cnoidal wave interaction solution in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral is obtained by using the consistent tanh expansion (CTE) method, which is a special form of CRE.

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35

WINKLER, R., and U. ZÜLICKE. "DISCRETE SYMMETRIES OF LOW-DIMENSIONAL DIRAC MODELS: A SELECTIVE REVIEW WITH A FOCUS ON CONDENSED-MATTER REALIZATIONS." ANZIAM Journal 57, no. 1 (2015): 3–17. http://dx.doi.org/10.1017/s1446181115000115.

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The most fundamental characteristic of a physical system can often be deduced from its behaviour under discrete symmetry transformations, such as time reversal, parity and chirality. Here, we review some of the basic symmetry properties of the relativistic quantum theories for free electrons in ($2+1$)- and ($1+1$)-dimensional spacetime. Additional flavour degrees of freedom are necessary to properly define symmetry operations in ($2+1$) dimensions, and are generally present in physical realizations of such systems, for example in single sheets of graphite. We find that there exist two possibilities for defining any flavour-coupling discrete symmetry operation of the two-flavour ($2+1$)-dimensional Dirac theory. Some physical implications of this previously unnoticed duplicity are discussed.

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36

Ray, S. Saha. "Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky–Konopelchenko equation by geometric approach." Modern Physics Letters B 32, no. 11 (2018): 1850127. http://dx.doi.org/10.1142/s0217984918501270.

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In this paper, the symmetry analysis and similarity reduction of the (2[Formula: see text]+[Formula: see text]1)-dimensional Bogoyavlensky–Konopelchenko (B–K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation is obtained.

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37

Wang, Gangwei, Li Li, Qi Wang, and Juan Geng. "New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form." Fractal and Fractional 6, no. 3 (2022): 166. http://dx.doi.org/10.3390/fractalfract6030166.

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In this paper, the extended double (2+1)-dimensional sine-Gorden equation is studied. First of all, using the symmetry method, the corresponding vector fields, Lie algebra and infinitesimal generators are derived. Then, from infinitesimal generators, the symmetry reductions are presented. In addition, these reduced equations are converted into the corresponding partial differential equations, which including classical double (1+1)-dimensional sine-Gorden equation. Moreover, based on the Lie symmetry method again, these reduced equations are investigated. Meanwhile, based on traveling wave transformation, some explicit solutions of the extended double (2+1)-dimensional sine-Gorden equation are obtained. Consequently, a conservation law is derived via conservation law multiplier method. Finally, especially with the help of the fractional complex transform, some solutions of double time fractional (2+1)-dimensional sine-Gorden equation are also derived. These results might explain complex nonlinear phenomenon.

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38

Huang, Jia-Hui, Guang-Zhou Guo, Hao-Yu Xie, Qi-Shan Liu, and Fang-Qing Deng. "Spontaneous breaking of (2 + 1)-dimensional Lorentz symmetry by an antisymmetric tensor." Modern Physics Letters A 33, no. 02 (2018): 1850007. http://dx.doi.org/10.1142/s0217732318500074.

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One kind of spontaneous (2 + 1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is SO(2, 1) [Formula: see text] SO(1, 1). Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu–Goldstone bosons is obtained.

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39

KOVNER, A. "MAGNETIC ZN SYMMETRY IN 2+1 DIMENSIONS." International Journal of Modern Physics A 17, no. 16 (2002): 2113–64. http://dx.doi.org/10.1142/s0217751x02010789.

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This review describes the role of magnetic symmetry in (2+1)-dimensional gauge theories. In confining theories without matter fields in fundamental representation the magnetic symmetry is spontaneously broken. Under some mild assumptions, the low-energy dynamics is determined universally by this spontaneous breaking phenomenon. The degrees of freedom in the effective theory are magnetic vortices. Their role in confining dynamics is similar to that played by pions and σ in the chiral symmetry breaking dynamics. I give an explicit derivation of the effective theory in (2+1)-dimensional weakly coupled confining models and argue that it remains qualitatively the same in strongly coupled (2+1)-dimensional gluodynamics. Confinement in this effective theory is a very simple classical statement about the long range interaction between topological solitons, which follows (as a result of a simple direct classical calculation) from the structure of the effective Lagrangian. I show that if fundamentally charged dynamical fields are present the magnetic symmetry becomes local rather than global. The modifications to the effective low energy description in the case of heavy dynamical fundamental matter are discussed. This effective Lagrangian naturally yields a bag like description of baryonic excitations. I also discuss the fate of the magnetic symmetry in gauge theories with the Chern–Simons term.

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HU, YING, and ZHAOXIN LIANG. "DIMENSIONAL CROSSOVER AND DIMENSIONAL EFFECTS IN QUASI-TWO-DIMENSIONAL BOSE GASES." Modern Physics Letters B 27, no. 14 (2013): 1330010. http://dx.doi.org/10.1142/s021798491330010x.

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This paper gives a systematic review on studies of dimensional effects in pure- and quasi-two-dimensional (2D) Bose gases, focusing on the role of dimensionality in the fundamental relation among the universal behavior of breathing mode, scale invariance and dynamic symmetry. First, we illustrate the emergence of universal breathing mode in the case of pure 2D Bose gases, and elaborate on its connection with the scale invariance of the Hamiltonian and the hidden SO(2, 1) symmetry. Next, we proceed to quasi-2D Bose gases, where excitations are frozen in one direction and the scattering behavior exhibits a 3D to 2D crossover. We show that the original SO(2, 1) symmetry is broken by arbitrarily small 2D effects in scattering, which consequently shifts the breathing mode from the universal frequency. The predicted shift rises significantly from the order of 0.5% to more than 5% in transiting from the 3D-scattering to the 2D-scattering regime. Observing this dimensional effect directly would present an important step in revealing the interplay between dimensionality and quantum fluctuations in quasi-2D.

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41

Kamath, Gopinath. "Cylindrical symmetry: II. The Green's function in 3+ 1 dimensional curved space." EPJ Web of Conferences 182 (2018): 03005. http://dx.doi.org/10.1051/epjconf/201818203005.

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An exact solution to the heat equation in curved space is a much sought after; this report presents a derivation wherein the cylindrical symmetry of the metric gμν in 3 + 1 dimensional curved space has a pivotal role. To elaborate, the spherically symmetric Schwarzschild solution is a staple of textbooks on general relativity; not so perhaps, the static but cylindrically symmetric ones, though they were obtained almost contemporaneously by H. Weyl, Ann. Phys. Lpz. 54, 117 (1917) and T. Levi-Civita, Atti Acc. Lincei Rend. 28, 101 (1919). A renewed interest in this subject in C.S. Trendafilova and S.A. Fulling, Eur.J.Phys. 32, 1663(2011) - to which the reader is referred to for more references - motivates this work, the first part of which (cf.Kamath, PoS (ICHEP2016) 791) reworked the Antonsen-Bormann idea - arXiv:hep-th/9608141v1 - that was originally intended to compute theheat kernel in curved space to determine - following D.McKeon and T.Sherry, Phys. Rev. D 35, 3584 (1987) - the zeta-function associated with the Lagrangian density for a massive real scalar field theory in 3 + 1 dimensional stationary curved space to one-loop order, the metric for which is cylindrically symmetric. Using the same Lagrangian density the second part reported here essentially revisits the second paper by Bormann and Antonsen - arXiv:hep 9608142v1 but relies on the formulation by the author in S. G. Kamath, AIP Conf.Proc.1246, 174 (2010) to obtain the Green's function directly by solving a sequence of first order partial differential equations that is preceded by a second order partial differential equation.

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Bakhshandeh-Chamazkoti, Rohollah. "Geometry of the curved traversable wormholes of (3 + 1)-dimensional spacetime metric." International Journal of Geometric Methods in Modern Physics 14, no. 04 (2017): 1750048. http://dx.doi.org/10.1142/s0219887817500487.

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In this paper, Noether symmetry and Killing symmetry analyses of the curved traversable wormholes of [Formula: see text]-dimensional spacetime metric in a Riemannian space are discussed. Moreover, a Lie algebra analysis is shown. Using the first and second Cartan’s structure equations, we find connection forms and then the curvature 2-forms are obtained. Finally, the Ricci scalar tensor and the components of Einstein curvature are computed.

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TAYLOR, STEPHEN, and SCOTT GLASGOW. "A NOVEL REDUCTION OF THE SIMPLE ASIAN OPTION AND LIE-GROUP INVARIANT SOLUTIONS." International Journal of Theoretical and Applied Finance 12, no. 08 (2009): 1197–212. http://dx.doi.org/10.1142/s0219024909005634.

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We develop the complete 6-dimensional classical symmetry group of the partial differential equation (PDE) that governs the fair price of a simple Asian option within a simple market model. The symmetries we expose include the 5-dimensional symmetry group partially noted by Rogers and Shi, and communicated implicitly by the change of numéraire arguments of Večeř (in which symmetries reduce the original 2 + 1 dimensional simple Asian option PDE to a 1 + 1 dimensional PDE). Going beyond this previous work, we expose a new 1-dimensional space of symmetries of the Asian PDE that cannot reasonably be found by inspection. We demonstrate that the new symmetry could be used to formulate a new, "nonlinear" derivative security that has a 1 + 1 dimensional PDE formulation. We indicate that this nonlinear security has a closed-form pricing formula similar to that of the Black–Scholes equation for a particular market dependent payoff, and show that hedging the short position in this particular exotic option is stable for all market parameters. We also demonstrate the patently Lie-algebraic method for obtaining the already well-known "Rogers–Shi–Večeř" reduction.

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Ray, S. Saha. "Optimal subalgebra, conservations laws and symmetry reductions with analytical solutions using Lie symmetry analysis and geometric approach for the (1+1)-dimensional Manakov model." Physica Scripta 98, no. 4 (2023): 045214. http://dx.doi.org/10.1088/1402-4896/acb7d2.

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Abstract In this article, the (1+1)-dimensional Manakov model has been examined for finding its exact closed form solitonic solutions with the help of symmetry generators. These symmetry generators are explored using the Lie symmetry analysis, commonly known as the classical Lie group approach and the geometric approach. In a geometric approach, the extended Harrison and Estabrook’s differential forms have been used for obtaining the infinitesimal generators of the Manakov model. As there are infinite possibilities for the linear combination of infinitesimal generators, so by using Olver’s standard approach a one-dimensional optimal system of subalgebra has been established. Additionally, the ‘new conservation theorem’ put forth by Ibragimov has been utilized in order to devise the conservation laws for the (1+1)-dimensional Manakov model. Finally, the exact closed form solutions are obtained with the help of Lie symmetries corresponding to the defined model.

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Szangolies, Jochen. "The Standard Model Symmetry and Qubit Entanglement." Entropy 27, no. 6 (2025): 569. https://doi.org/10.3390/e27060569.

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Research at the intersection of quantum gravity and quantum information theory has seen significant success in describing the emergence of spacetime and gravity from quantum states whose entanglement entropy approximately obeys an area law. In a different direction, the Kaluza–Klein proposal aims to recover gauge symmetries by means of dimensional reduction in higher-dimensional gravitational theories. Integrating both of these, gravitational and gauge degrees of freedom in 3+1 dimensions may be obtained upon dimensional reduction in higher-dimensional emergent gravity. To this end, we show that entangled systems of two and three qubits can be associated with 5+1- and 9+1-dimensional spacetimes, respectively, which are reduced to 3+1 dimensions upon singling out a preferred complex direction. Depending on the interpretation of the residual symmetry, either the Standard Model gauge group, SU(3)×SU(2)×U(1)/Z6, or the symmetry of Minkowski spacetime together with the gauge symmetry of a right-handed ‘half-generation’ of fermions can be recovered. Thus, there seems to be a natural way to accommodate the chirality of the weak force in the given construction. This motivates a picture in which spacetime emerges from the area law contribution to the entanglement entropy, while gauge and matter degrees of freedom are obtained due to area-law-violating terms. Furthermore, we highlight the possibility of using this construction in quantum simulations of Standard Model fields.

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XU, KAI-WEN, and CHUAN-JIE ZHU. "SYMMETRY IN TWO-DIMENSIONAL GRAVITY." International Journal of Modern Physics A 06, no. 13 (1991): 2331–46. http://dx.doi.org/10.1142/s0217751x91001143.

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We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL (2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl (2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

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Li, Wenting, Yueting Chen, and Kun Jiang. "Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations." Symmetry 15, no. 12 (2023): 2199. http://dx.doi.org/10.3390/sym15122199.

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In this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By solving the governing equations that satisfy this condition, we can obtain the corresponding reduced equation. This allows us to determine the non-classical symmetry of the differential–difference equation. This method avoids the complicated calculation involved in extending the infinitesimal generator and allows for a wider range of symmetry forms. As a result, it enables the derivation of a greater number of differential–difference equations. In this paper, two kinds of (2+1)-dimensional Toda-like lattice equations are taken as examples, and their corresponding symmetric and reduced equations are obtained using the non-classical symmetry method.

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WATABIKI, YOSHIYUKI. "REMARKS ON THE MODEL WITH LOCAL U(1)V×U(1)A SYMMETRY IN TWO DIMENSIONS." Modern Physics Letters A 06, no. 14 (1991): 1291–98. http://dx.doi.org/10.1142/s021773239100138x.

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We investigate a 2-dimensional model which possesses a local vector U (1)V and axial vector U (1)A symmetry. We obtain a general form of Lagrangian which possesses this local symmetry. We also investigate the global symmetry aspects of the model. The commutator algebra of the energy-momentum tensor and the currents is derived, and the central charge of the model is calculated. Supersymmetric extension of the model is also studied.

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Dong, Zhong Zhou, and Yong Chen. "Symmetry Reduction, Exact Solutions, and Conservation Laws of the (2+1)-Dimensional Dispersive Long Wave Equations." Zeitschrift für Naturforschung A 64, no. 9-10 (2009): 597–603. http://dx.doi.org/10.1515/zna-2009-9-1009.

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By means of the generalized direct method, we investigate the (2+1)-dimensional dispersive long wave equations. A relationship is constructed between the new solutions and the old ones and we obtain the full symmetry group of the (2+1)-dimensional dispersive long wave equations, which includes the Lie point symmetry group S and the discrete groups D. Some new forms of solutions are obtained by selecting the form of the arbitrary functions, based on their relationship. We also find an infinite number of conservation laws of the (2+1)-dimensional dispersive long wave equations.

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ALMUKAHHAL, RAJA Q., and TRISTAN HÜBSCH. "GAUGING YANG–MILLS SYMMETRIES IN (1+1)-DIMENSIONAL SPACE–TIME." International Journal of Modern Physics A 16, no. 29 (2001): 4713–68. http://dx.doi.org/10.1142/s0217751x01005523.

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We present a systematic and "from the ground up" analysis of the "minimal coupling" type of gauging of Yang–Mills symmetries in (2, 2)-supersymmetric (1+1)-dimensional space–time. Unlike in the familiar (3+1)-dimensional N=1 supersymmetric case, we find several distinct types of minimal coupling symmetry gauging, and so several distinct types of gauge (super)fields, some of which entirely novel. Also, we find that certain (quartoid) constrained superfields can couple to no gauge superfield at all, others (haploid ones) can couple only very selectively, while still others (nonminimal, i.e. linear ones) couple universally to all gauge superfields.

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