Action of the loop group on the self-dual Yang-Mills equation
type: Item
instance of: scholarly article
title: Action of the loop group on the self-dual Yang-Mills equation
zbMATH Open document ID: 0638.58028
DOI: 10.1007/BF01212419
author: Louis Crane
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: Recently Kac-Moody symmetry has played an important role in mathematical physics. Dolan and Chau, Ge and Wu discovered an infinitesimal action of the Kac-Moody Lie algebra on the space of solutions of SDYM (self dual Yang-Mills equation). We have discovered an action of the loop group on the space of generalized solutions of SDYM, which exponentiates the Kac- Moody action. The group acts by adding a special type of source onto the solution. The action is a geometric construction using the twistor picture.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 35Q15
zbMATH DE Number: 4040893
zbMATH Keywords: Kac-Moody symmetry
zbMATH Keywords: infinitesimal action of the Kac-Moody Lie algebra
zbMATH Keywords: loop group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4040893