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Journal articles on the topic '1-dimensional symmetry'

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Published: 9 March 2023

Last updated: 11 March 2023

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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 (July 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 (May 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 (December 20, 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

Oshima, Kazuto. "Spontaneous Symmetry Breaking in (1+1)-Dimensional Light-Front φ4Theory." Journal of the Physical Society of Japan 72, no. 1 (January 15, 2003): 83–88. http://dx.doi.org/10.1143/jpsj.72.83.

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5

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

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6

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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7

Babu, K. S., P. Panigrahi, and S. Ramaswamy. "Radiative symmetry breaking in (2+1)-dimensional space." Physical Review D 39, no. 4 (February 15, 1989): 1190–95. http://dx.doi.org/10.1103/physrevd.39.1190.

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8

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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9

SINHA, A., and P. ROY. "(1+1)-DIMENSIONAL DIRAC EQUATION WITH NON-HERMITIAN INTERACTION." Modern Physics Letters A 20, no. 31 (October 10, 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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10

Kotikov, Anatoly V., and Sofian Teber. "Critical Behavior of (2 + 1)-Dimensional QED: 1/N Expansion." Particles 3, no. 2 (April 10, 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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11

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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12

Lin, Ji. "(3+1)-Dimensional Integrable Models Possessing Infinite Dimensional Virasoro-Type Symmetry Algebra." Communications in Theoretical Physics 25, no. 4 (June 15, 1996): 447–50. http://dx.doi.org/10.1088/0253-6102/25/4/447.

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13

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 (May 1995): 47–52. http://dx.doi.org/10.1016/0375-9601(95)00201-d.

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14

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 (October 2009): 1141–45. http://dx.doi.org/10.1016/j.amc.2009.06.049.

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15

HALL, BRIAN C. "COHERENT STATES AND THE QUANTIZATION OF (1+1)-DIMENSIONAL YANG–MILLS THEORY." Reviews in Mathematical Physics 13, no. 10 (October 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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16

ARIK, METIN, and MUHITTIN MUNGAN. "SYMMETRY CHANGES DURING THE EVOLUTION OF THE UNIVERSE." Modern Physics Letters A 05, no. 31 (December 20, 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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17

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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18

Qu, Chang-Zheng. "Symmetry Algebras of Generalized (2 + 1)-Dimensional KdV Equation." Communications in Theoretical Physics 25, no. 3 (April 30, 1996): 369–72. http://dx.doi.org/10.1088/0253-6102/25/3/369.

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19

Polychronakos, Alexios P. "Symmetry-Breaking Patterns in (2+1)-Dimensional Gauge Theories." Physical Review Letters 60, no. 19 (May 9, 1988): 1920–23. http://dx.doi.org/10.1103/physrevlett.60.1920.

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20

Zhao, Jing. "SYMMETRY ANALYSIS OF THE 2 + 1 DIMENSIONAL DIFFUSION EQUATION." Far East Journal of Applied Mathematics 94, no. 1 (January 12, 2016): 55–62. http://dx.doi.org/10.17654/am094010055.

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21

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 (March 23, 1995): L191—L196. http://dx.doi.org/10.1088/0305-4470/28/6/002.

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22

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 (May 29, 2008): 1927–30. http://dx.doi.org/10.1088/0256-307x/25/6/002.

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23

Tobita, Yutaka, and Jun Goryo. "Tobological feedback for superconducting states." Journal of Physics: Conference Series 2164, no. 1 (March 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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24

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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25

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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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 (June 22, 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

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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28

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 (October 1, 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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29

WU, YUE-LIANG. "MAXIMALLY SYMMETRIC MINIMAL UNIFICATION MODEL SO(32) WITH THREE FAMILIES IN TEN-DIMENSIONAL SPACETIME." Modern Physics Letters A 22, no. 04 (February 10, 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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30

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 (January 19, 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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31

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 (December 3, 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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32

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 (July 1, 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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33

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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34

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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35

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 (March 8, 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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36

Ma, Hong-Cai, Ai-Ping Deng, and Yao-Dong Yu. "Lie symmetry group of (2+1)-dimensional Jaulent-Miodek equation." Thermal Science 18, no. 5 (2014): 1547–52. http://dx.doi.org/10.2298/tsci1405547m.

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In this paper, we consider a system of (2+1)-dimensional non-linear model by using auxiliary equation method and Clarkson-Kruskal direct method which is very important in fluid and physics. We construct some new exact solutions of (2+1)-dimensional non-linear models with the aid of symbolic computation which can illustrate some actions in fluid in the future.

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37

LOU SEN-YUE, YU JUN, WENG JIAN-PIN, and QIAN XIAN-MIN. "SYMMETRY STRUCTURE OF 2+1 DIMENSIONAL BILINEAR SAWADA-KOTERA EQUATION." Acta Physica Sinica 43, no. 7 (1994): 1050. http://dx.doi.org/10.7498/aps.43.1050.

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38

Hu, Heng-Chun, Jing-Bo Wang, and Hai-Dong Zhu. "Symmetry Reduction of (2+1)-Dimensional Lax-Kadomtsev-Petviashvili Equation." Communications in Theoretical Physics 63, no. 2 (February 2015): 136–40. http://dx.doi.org/10.1088/0253-6102/63/2/03.

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39

Kudryavtsev, A. G., and N. N. Myagkov. "Symmetry group application for the (3+1)-dimensional Rossby waves." Physics Letters A 375, no. 3 (January 2011): 586–88. http://dx.doi.org/10.1016/j.physleta.2010.11.040.

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40

Hong-Cai, Ma, and Lou Sen-Yue. "Non-Lie Symmetry Groups of (2+1)-Dimensional Nonlinear Systems." Communications in Theoretical Physics 46, no. 6 (December 2006): 1005–10. http://dx.doi.org/10.1088/0253-6102/46/6/010.

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41

Xiao-Yan, Tang, and Lou Sen-Yue. "Symmetry Analysis of (2+1)-Dimensional Nonlinear Klein-Gordon Equations." Chinese Physics Letters 19, no. 1 (December 19, 2001): 1–3. http://dx.doi.org/10.1088/0256-307x/19/1/301.

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42

Osborn, Hugh. "N=1 Superconformal Symmetry in Four-Dimensional Quantum Field Theory." Annals of Physics 272, no. 2 (March 1999): 243–94. http://dx.doi.org/10.1006/aphy.1998.5893.

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43

KOVNER, A. "MAGNETIC ZN SYMMETRY IN 2+1 DIMENSIONS." International Journal of Modern Physics A 17, no. 16 (June 30, 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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44

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 (November 20, 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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XU, KAI-WEN, and CHUAN-JIE ZHU. "SYMMETRY IN TWO-DIMENSIONAL GRAVITY." International Journal of Modern Physics A 06, no. 13 (May 30, 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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HU, YING, and ZHAOXIN LIANG. "DIMENSIONAL CROSSOVER AND DIMENSIONAL EFFECTS IN QUASI-TWO-DIMENSIONAL BOSE GASES." Modern Physics Letters B 27, no. 14 (May 16, 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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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 (April 1, 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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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 (July 10, 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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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 (April 18, 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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KOVNER, A., B. ROSENSTEIN, and D. ELIEZER. "PHOTON AS GOLDSTONE BOSON IN (2 + 1)-DIMENSIONAL HIGGS MODEL." Modern Physics Letters A 05, no. 32 (December 30, 1990): 2733–40. http://dx.doi.org/10.1142/s0217732390003188.

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We examine the relationship between the masslessness of a photon and symmetry realizations in (2 + 1)-dimensional scalar QED. We find that this masslessness is a direct consequence of spontaneous breaking of a global symmetry, whose generator is the magnetic flux. The pertinent order parameter for the Higgs-Coulomb phase transition is identified with the VEV of the magnetic vortex creation operator V(x). We calculate, using weak coupling perturbation theory, the VEV and the correlator of V(x) in both phases. This turns out to be equivalent to evaluating the Euclidean QED partition function in the presence of the external current which produces a magnetic monopole (with the contribution of the Dirac string subtracted). In the Coulomb phase <V(x)> is finite, while in the Higgs phase it vanishes.

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