Parastatistics, highest weight \(\mathrm{osp}(N,\infty)\) modules, singleton statistics and confinement
type: Item
instance of: scholarly article
title: Parastatistics, highest weight \(\mathrm{osp}(N,\infty)\) modules, singleton statistics and confinement
zbMATH Open document ID: 0689.17003
DOI: 10.1016/0393-0440(89)90018-1
author: Moshé Flato
author: Christian Frønsdal
published in: Journal of Geometry and Physics
publication date: 1989-01-01T00:00:00Z
review text: The basic ideas and latest developments of parastatistics in the modern quantum field theory are reviewed and some generalizations of this approach are suggested. Since the structure of parabose statistics is determined by the infinite dimensional orthosymplectic Lie super algebra \(\mathrm{osp}(N,\infty)\), the Fock spaces of parastatistics are interpreted as the unitarizable highest weight modules with the degenerate highest weight space (vacuum). It is pointed out that the other hermitian representations of \(\mathrm{osp}(1,\infty)\) may be applied for description of symmetry breakdown. The alternative possibilities of using in parastatistics the so called ``extended orthosymplectic'' superalgebras \((N,2n)\) and \((N,\infty)\) are also considered. In conclusion the problems of compositeness and confinement in the framework of singletons (obeying parastatistics) are briefly discussed.
reviewed by: A. A. Bogush
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 81S05
Mathematics Subject Classification ID: 81V05
zbMATH DE Number: 4129023
zbMATH Keywords: parastatistics
zbMATH Keywords: orthosymplectic Lie superalgebra
zbMATH Keywords: Fock spaces
zbMATH Keywords: highest weight modules
zbMATH Keywords: confinement
zbMATH Keywords: singletons
MaRDI profile type: Publication
full work available at URL: 0393-0440(89)90018-1
OpenAlex ID: W2093439173
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description: scientific article; zbMATH DE number 4129023