The star exponential and path integrals on compact groups. II: The Weyl character formula
type: Item
instance of: scholarly article
title: The star exponential and path integrals on compact groups. II: The Weyl character formula
zbMATH Open document ID: 0795.58008
DOI: 10.1007/BF00939699
author: V. Pereyra
published in: Letters in Mathematical Physics
publication date: 1994-03-22T00:00:00Z
review text: Let \(G\) be a compact simply connected Lie group and let \(H \subset G\) be a maximal torus. By using Borel-Weil-Bott construction of a holomorphic line bundle and the space of holomorphic sections with a metric, the associated unitary irreducible representation and the dequantization procedure of Berezin, the author in collaboration with \textit{A. C. Cadavid} [part I of this paper, ibid. 23, No. 2, 111-115 (1991; Zbl 0747.58019)] defined a \(G\)-invariant star product. In the present work an expression for the Weyl character formula is obtained in terms of the star product path integral. The relationship between path integrals constructed with the star product and with coadjoint orbits is also studied.
reviewed by: Chandra Shekhar Sharma
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 81S10
Mathematics Subject Classification ID: 81S40
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 81T70
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 43A77
zbMATH DE Number: 536882
zbMATH Keywords: compact groups
zbMATH Keywords: Weyl character formula
zbMATH Keywords: path integrals
zbMATH Keywords: star product
MaRDI profile type: Publication
cites work: The star exponential and path integrals on compact groups
cites work: Kirillov-Kostant theory and Feynman path integrals on coadjoint orbits. I
cites work: Kirillov-Kostant theory and Feynman path integrals on coadjoint orbits of SU(2) and SU(1,1)
cites work: Borel-Weil theory and Feynman path integrals on flag manifolds
cites work: Q4451321
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description: scientific article; zbMATH DE number 536882