Gauge theories, flat superforms and reduction of super fiber bundles
type: Item
instance of: scholarly article
title: Gauge theories, flat superforms and reduction of super fiber bundles
zbMATH Open document ID: 0654.58036
DOI: 10.1016/0034-4877(88)90042-0
author: Massimo Grasso
author: Paolo Teofilatto
published in: Reports on Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: Connection superforms defined on super fiber bundles represent fields of both supersymmetric and non-supersymmetric quantized gauge theories, provided that some constraint equations on connections are imposed. In this paper we investigate the geometrical meaning of these constraint equations in such a way that we can recognize certain classes of connection superforms as the suitable ones to represent the fields of these gauge theories. Moreover, the existence of such classes of connections implies a reduction of the involved super fiber bundles to the effective spaces on wemes is a response to this question. We introduce a class of modules which generalizes the idea of a projective module, and which is particularly relevant to the applications of representation theory to translation planes.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 4067926
zbMATH Keywords: Connection superforms
zbMATH Keywords: super fiber bundles
zbMATH Keywords: quantized gauge theories
zbMATH Keywords: projective module
MaRDI profile type: Publication
full work available at URL: 0034-4877(88)90042-0
OpenAlex ID: W2035386619
cites work: Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras
cites work: Superspaces and supersymmetries
cites work: Supermanifolds and BRS transformations
cites work: Q3344780
cites work: Mathematical theory of super fibre bundles
cites work: Generalized supermanifolds. I. Superspaces and linear operators
cites work: On the body of supermanifolds
cites work: Global properties of supermanifolds
cites work: How different are the supermanifolds of Rogers and De Witt?
cites work: The theory of Lie superalgebras. An introduction
cites work: Q4746527
cites work: Foliated bundles and characteristic classes
cites work: Q5731354
cites work: On the existence of global integral forms on supermanifolds
cites work: Super Lie groups: global topology and local structure
cites work: An existence result for super Lie groups
cites work: Differential equations, Frobenius theorem and local flows on supermanifolds
cites work: Superanalysis, I. Differential calculus
Recommended article: Q4725368
Recommended article: Q3996986
Recommended article: Quantized super-Yang - Mills theory in the superfibre bundle approach
Recommended article: Supersymmetric Gauge Theories, Quantization of $${\mathcal M}_\mathrm{flat}$$ , and Conformal Field Theory
Recommended article: Gauge and matter superfield theories on \(S^{2}\)
Recommended article: Cohomological aspects of gauge theories: Superfield formalism.
Recommended article: Gauge fields in superspace and twistors
Recommended article: Supersymmetric gauge theories, vortices and equivariant cohomology
Recommended article: Q3756958
Recommended article: Supersymmetric gauge theories, quantization of \(\mathcal{M}_{\text{flat}}\), and conformal field theory
description: scientific article; zbMATH DE number 4067926