Quantum stochastic calculus and representations of Lie superalgebras
type: Item
instance of: scholarly article
title: Quantum stochastic calculus and representations of Lie superalgebras
zbMATH Open document ID: 0922.60004
author: Timothy M. W. Eyre
published in: Lecture Notes in Mathematics
publication date: 1998-10-06T00:00:00Z
review text: The monograph treats a generalization of the relation between bosonic and fermionic stochastic calculi, which gives rise to a \({\mathbb Z}_2\)-graded theory of multi-dimensional quantum stochastic calculus. In this theory one has a mixture of multi-dimensional bosonic and fermionic creation and annihilation processes along with \({\mathbb Z}_2\)-graded multi-dimensional gauge process. The commutation and anticommutation properties of these processes are shown to provide a time-indexed family of representations of a broad class of Lie superalgebras. The Lie superalgebra representation result is used to derive a formula for chaotic decomposition of elements of the universal enveloping superalgebra of the Lie superalgebra associated with \({\mathbb Z}_2\)-graded quantum stochastic calculus. It is suggested that this calculus may be useful in the theory of quantum groups.
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 81S25
Mathematics Subject Classification ID: 60K99
Mathematics Subject Classification ID: 81-02
zbMATH DE Number: 1206421
zbMATH Keywords: quantum stochastic calculus
zbMATH Keywords: Lie superalgebra
MaRDI profile type: Publication
DOI: 10.1007/BFB0096850
reviewed by: Alexander S. Holevo
description: scientific article; zbMATH DE number 1206421