Analytic vectors, anomalies and star representations
type: Item
instance of: scholarly article
title: Analytic vectors, anomalies and star representations
zbMATH Open document ID: 0692.22012
DOI: 10.1007/BF00402326
author: Carlos Alcalde
author: Daniel Sternheimer
published in: Letters in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The paper starts by reviewing the notion of analytic vectors and local representations of Lie algebras (i.e. non-integrable to the Lie group). The authors show in simple examples (one is the Heisenberg algebra acting on the space of square integrable functions on the circle) that local representations are in fact anomalous representations due to the lack of common analytic vectors which is produced by the topological nontriviality of its phase-space. To avoid these anomalies they propose to use a quantization which exploits the geometry of phase-space, e.g. star-quantization, which means a deformation of the algebra of observables in phase-space (a new - in general noncommutative - product law between functions in phase-space is introduced). In the above example this means replacing the Heisenberg algebra by the Euclidean algebra. They finally apply these ideas to simple two-dimensional field-theoretical models.
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 17B15
Mathematics Subject Classification ID: 81Q99
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 4132481
zbMATH Keywords: analytic vectors
zbMATH Keywords: local representations of Lie algebras
zbMATH Keywords: Heisenberg algebra
zbMATH Keywords: square integrable functions
zbMATH Keywords: anomalous representations
zbMATH Keywords: phase- space
zbMATH Keywords: quantization
zbMATH Keywords: field-theoretical models
reviewed by: Evelyn Weimar-Woods
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4132481