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Variational Principles of General Connections with a Certain Deformation of Representations

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Abstract

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.

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Acknowledgements

I would like to express my gratitude to professor Akira Yoshioka for his valuable advices and suggestions.

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  1. Department of Mathematics, Tokyo University of Science, Kagurazaka 1-3, Shinjuku-ku, Tokyo, 162-8601, Japan

    Kensaku Kitada

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  1. Kensaku Kitada
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Correspondence to Kensaku Kitada.

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Kitada, K. Variational Principles of General Connections with a Certain Deformation of Representations. Results Math 74, 184 (2019). https://doi.org/10.1007/s00025-019-1108-6

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