A Possible Description of Many-Body System Composed of Four Kinds of Boson Operators: In Relation to the su(2)- and the su(1, 1)-Algebraic Model

Kuriyama, Atsushi; Providência, João da; Yamamura, Masatoshi

doi:10.1143/ptp.103.305

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“…Boson realizations arise naturally when considering the groups Sp(2n, R), SU(n) and some of their subgroups. For instance, SU(1, 1), SU (2) and SU(3) boson realizations are used to study degeneracies, symmetries and dynamics in quantum systems [33][34][35][36][37][38][39][40][41] . A wide class of problems in theoretical physics rely on boson realizations of the symplectic group [42][43][44][45][46] .…”

Section: Introductionmentioning

confidence: 99%

Algorithms for SU(n) boson realizations and D-functions

Dhand

Sanders

Guise

2015

Journal of Mathematical Physics

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Boson realizations map operators and states of groups to transformations and states of bosonic systems. We devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU(n) basis states, which reduce the canonical subgroup chain, for arbitrary n. The boson realizations are employed to construct D-functions, which are the matrix elements of arbitrary irreducible representations, of SU(n) in the canonical basis. We demonstrate that our D-function algorithm offers significant advantage over the two competing procedures, namely factorization and exponentiation.

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