An Overview of the Relationship between Group Theory and Representation Theory to the Special Functions in Mathematical Physics

Wasson, Ryan D.; Gilmore, Robert

doi:10.48550/arxiv.1309.2544

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“…In our present study for large B we derived operators ˆA L ± of the angular momentum, which includes an additional term in comparison with the conventional one. This term is well known in fields of mathematical physics, where relations between the generalized SU(2) algebra and the special functions [46] [49] [50] were studied. Our ˆA L ± and Lφ operators show the generalized algebra, which is called the spinweighed harmonics.…”

Section: Summary and Discussionmentioning

confidence: 99%

Degenerate States in Nonlinear Sigma Model with SU(2) Symmetry

Munehisa¹

2023

WJCMP

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Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.

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Section: Summary and Discussionmentioning

confidence: 99%

Degenerate States in Nonlinear Sigma Model with SU(2) Symmetry

Munehisa¹

2023

WJCMP

View full text Add to dashboard Cite

show abstract

An Overview of the Relationship between Group Theory and Representation Theory to the Special Functions in Mathematical Physics

Cited by 1 publication

References 4 publications

Degenerate States in Nonlinear Sigma Model with SU(2) Symmetry

Degenerate States in Nonlinear Sigma Model with SU(2) Symmetry

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