Variational Principles of General Connections with a Certain Deformation of Representations

We investigate variational principles of general connections on principal bundles. In order to develop further a gauge theory by means of general connections, we introduce a certain deformation of representations of the structure group. This enables us to define exterior covariant derivatives on a s...

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Bibliographic Details
Published inResultate der Mathematik Vol. 74; no. 4
Main Author Kitada, Kensaku
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2019
Subjects
Mathematics
Mathematics and Statistics
variational principle
58E15
Higgs mechanism
inhomogeneous field equation
General connection
current conservation law
53C05
58E30
Lagrange’s equation
53C80
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Summary:We investigate variational principles of general connections on principal bundles. In order to develop further a gauge theory by means of general connections, we introduce a certain deformation of representations of the structure group. This enables us to define exterior covariant derivatives on a space of sort of shifted fields. We construct action densities by using general connections, and deduce a sort of Lagrange’s equation and that of inhomogeneous field equation simultaneously. Due to the definition of the curvature of general connections, a new term will arise in the latter equation, which we demonstrate later to be an obstruction for current conservation law to hold. Finally, we explain that a theory of general connections is a natural means to describe so-called Higgs mechanism.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-019-1108-6