Topic
Symmetry (physics)
About: Symmetry (physics) is a research topic. Over the lifetime, 26435 publications have been published within this topic receiving 500189 citations. The topic is also known as: symmetry (physics) & physical symmetry.
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01 Jan 1995
TL;DR: Inverse scattering and Darboux Transformations have been used in the theory of solitons as discussed by the authors for nonlinear nonlinear wave propagation, where the soliton theory and differential geometry have been combined.
Abstract: 1 Soliton Theory and Modern Physics.- 2 Inverse Scattering Methods.- 3 Backlund Transformations and Darboux Transformations.- 4 Classical Integrable Systems.- 5 Symmetry.- 6 Kac-Moody Algebras and Integrable Systems.- 7 Soliton and Differential Geometry.- 8 Numerical Study of Nonlinear Waves.- 9 Solitons in the Theory of Gravitational Waves.- References.
246 citations
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TL;DR: The results showed that, when using the symmetry index, the interpretation of asymmetry can be highly affected by the choice of reference value, and that the symmetry angle does not require a reference value and is not prone to the same limitations.
246 citations
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TL;DR: In this paper, a systematic way to construct symmetry-protected topological (SPT) states in interacting bosonic systems is presented, which allows us to identify many new SPT phases, including three bosonic versions of topological insulators in three dimensions and one in two dimensions protected by particle number conservation and time reversal symmetry.
Abstract: Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory. However, it is not known what SPT phases exist in general interacting systems. In this paper, we present a systematic way to construct SPT phases in interacting bosonic systems, which allows us to identify many new SPT phases, including three bosonic versions of topological insulators in three dimension and one in two dimension protected by particle number conservation and time reversal symmetry. Just as group theory allows us to construct 230 crystal structures in 3D, we find that group cohomology theory allows us to construct different interacting bosonic SPT phases in any dimensions and for any symmetry groups. In particular, we are going to show how topological terms in the path integral description of the system can be constructed from nontrivial group cohomology classes, giving rise to exactly soluble Hamiltonians, explicit ground state wave functions and symmetry protected gapless edge excitations.
245 citations
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TL;DR: In this paper, two massless non-diagonal scattering theories with SU(2) isotopic symmetry are proposed, and the thermodynamic Bethe ansatz equations are derived.
245 citations