String quantization on group manifolds and the holomorphic geometry of Diff \(S^ 1/S^ 1\)
type: Item
instance of: scholarly article
title: String quantization on group manifolds and the holomorphic geometry of Diff \(S^ 1/S^ 1\)
zbMATH Open document ID: 0629.58035
DOI: 10.1007/BF01225379
author: Jouko Mickelsson
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The recent results by Bowick and Rajeev on the relation of the geometry of Diff \(S^ 1/S^ 1\) and string quantization in \({\mathbb{R}}^{d,1}\) are extended to a string moving on a group manifold. A new derivation of the curvature formula \((-(26/12)m^ 3+(1/6)m)\delta_{n,-m}\) for the canonical holomorphic line bundle over Diff \(S^ 1/S^ 1\) is given which clarifies the relation of that bundle with the complex line bundles over infinite-dimensional Grassmannians, studied by Pressley and Segal.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 4024365
zbMATH Keywords: string quantization
zbMATH Keywords: string moving on a group manifold
MaRDI profile type: Publication
cites work: Semi-infinite cohomology and string theory
cites work: KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS
cites work: Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.
cites work: The inverse function theorem of Nash and Moser
cites work: Q3693672
cites work: Kac-Moody groups, topology of the Dirac determinant bundle, and fermionization
cites work: Q3754832
cites work: Non-Abelian bosonization in two dimensions
description: scientific article; zbMATH DE number 4024365