Indefinite harmonic forms and gauge theory
type: Item
instance of: scholarly article
title: Indefinite harmonic forms and gauge theory
zbMATH Open document ID: 0659.22013
DOI: 10.1007/BF01228413
author: S. H. Smith
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: A geometrical realization of the unitary highest weight representations of the conformal and the de Sitter groups (lying in the analytic continuation of the holomorphic discrete series) is given as the unitary quotient of an indecomposable representation using the indefinite harmonic forms [\textit{J. Rawnsley}, \textit{W. Schmid}, \textit{J. A. Wolf}, J. Funct. Anal. 51, 1-114 (1983; Zbl 0511.22005)]. The relation between these representations and the known massless, positive energy representations of SU(2,2) is established. It is demonstrated that this construction (after corresponding extension) allows to consider the twistor theory as a gauge field theory of SU(2,2). However such an approach is shown in the paper to be inapplicable to the gauge theory of the Dirac singletons based on the de Sitter group.
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 4077591
zbMATH Keywords: unitary highest weight representations
zbMATH Keywords: de Sitter groups
zbMATH Keywords: holomorphic discrete series
zbMATH Keywords: indefinite harmonic forms
zbMATH Keywords: representations of SU(2,2)
zbMATH Keywords: twistor theory
zbMATH Keywords: gauge field theory
zbMATH Keywords: Dirac singletons
reviewed by: A. A. Bogush
MaRDI profile type: Publication
cites work: Indecomposable representations with invariant inner product. A theory of the Gupta-Bleuler triplet
cites work: Wave equations in conformal space
cites work: A Remarkable Representation of the 3 + 2 de Sitter Group
cites work: Duality in twistor theory
cites work: The singleton dipole
cites work: The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
cites work: Indecomposable representations of the conformal group: A nonsingular photon-Weyl graviton system
cites work: Q3935911
cites work: Conformal quantum Yang–Mills
cites work: Q3966744
cites work: Q4207348
cites work: Conformal covariants
cites work: Q3713231
cites work: Yang-Mills fields and extension theory
cites work: Singular unitary representations and indefinite harmonic theory
cites work: Pseudo-Hermitian symmetric spaces
cites work: An ambitwistor description of bosonic or supersymmetric minimal surfaces and strings in four dimensions
cites work: Twistor quantisation of open strings in three dimensions
cites work: Complex manifolds and mathematical physics
cites work: Q3750679
description: scientific article; zbMATH DE number 4077591