Variational Principles of General Connections with a Certain Deformation of Representations
- 50 Downloads
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.
KeywordsGeneral connection variational principle Lagrange’s equation inhomogeneous field equation current conservation law Higgs mechanism
Mathematics Subject Classification58E30 58E15 53C05 53C80
I would like to express my gratitude to professor Akira Yoshioka for his valuable advices and suggestions.