Unitary group representations in Fock spaces with generalized exchange properties
type: Item
instance of: scholarly article
title: Unitary group representations in Fock spaces with generalized exchange properties
zbMATH Open document ID: 0835.22020
DOI: 10.1007/BF00750766
author: Yanyan Li
published in: Letters in Mathematical Physics
publication date: 1995-10-31T00:00:00Z
review text: Canonical commutation relations (CCR) form the basis of second quantization. There are instances where \(q\)-deformed CCR play an important role. In the present note the authors suggest to study \(R\)- deformed CCR, where \(R(x,y)\) is a complex-valued function on \(\mathbb{R}^s \times \mathbb{R}^s\): \[ a(x) a(y) - R(x,y) a(y) a(x) = \delta (x - y). \] The Fock representations of these relations are described. Central to this work is the \(R\)-quantization of operators, i.e., the way in which unitary operators \(V\) on the one-particle space are (functorially) extended to unitary operators on the entire Fock space. The claim, that the developed formalism is well adapted to deal with the problems of anyon field theory, has not been substantiated in a convincing manner.
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 81S05
zbMATH DE Number: 811311
zbMATH Keywords: canonical commutative relations
zbMATH Keywords: quantization
zbMATH Keywords: Fock representations
zbMATH Keywords: unitary operators
zbMATH Keywords: Fock space
zbMATH Keywords: anyon field theory
reviewed by: Gert Roepstorff
MaRDI profile type: Publication
cites work: Fock representations of quantum fields with generalized statistics
cites work: Fock spaces with generalized statistics
cites work: Q5653193
cites work: Q4066072
cites work: Superselection sectors with braid group statistics and exchange algebras
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description: scientific article; zbMATH DE number 811311