Boson representations of symplectic algebras
type: Item
instance of: scholarly article
title: Boson representations of symplectic algebras
zbMATH Open document ID: 0613.22008
DOI: 10.1007/BF00668689
author: B. George
published in: International Journal of Theoretical Physics
publication date: 1986-01-01T00:00:00Z
review text: The boson operators \(a_{\alpha i}\), \(a^+_{\alpha i}\) \((\alpha =1,2\); \(i=1,...,k)\) in their bilinear products generate, as is well known, the group Sp(4k, \({\mathbb{R}}):\{a^+_{\alpha i}a^+_{\beta j}\); \(a_{\alpha i}a_{\beta j}\), \(a^+_{\alpha i}a_{\beta j}\); \(\alpha,\beta =1,2\); \(i,j=1,...,k\}\). In this paper the subgroup chains \[ Sp(4k, {\mathbb{R}})\quad \to \quad U(2k)\quad \to \quad SU(2)\times SU(u)\quad \to \quad SU(k) \] \[ Sp(4k, {\mathbb{R}})\quad \to \quad U(k,k)\quad \to \quad U(k)\times U(k)\quad \to \quad SU(k) \] are considered, and the examples \(k=1\), \(k=2\), and \(k=3\) are analysed in detail.
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81T60
zbMATH DE Number: 3991802
zbMATH Keywords: symplectic algebras
zbMATH Keywords: group representations
zbMATH Keywords: dynamical groups
zbMATH Keywords: boson operators
reviewed by: A. O. Barut
MaRDI profile type: Publication
cites work: Group theory approach to scattering
cites work: Coupling problem for U(p, q) ladder representations. I
cites work: Irreducibility of the Ladder Representations of U(2, 2) when Restricted to the Poincaré Subgroup
cites work: Wigner Coefficients for the S U 3
cites work: The discrete series of \(Sp(n,\mathbb{R})\)
description: scientific article; zbMATH DE number 3991802