The Geometry of Gauge-Particle Field Interaction: A Generalization of Utiyama's Theorem

Document Type

Article

Publication Date

1-1-1989

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

The paper classifies the locally gauge invariant Lagrangians on the jet bundle J1 (E Θ C), for interacting particle and gauge fields. This serves to clarify the global nature of the Utiyama extension process (Yang-Mills trick) for arbitrary principal bundles P and gives the classical (local) results when P is trivial: P = M × G. The emphasis of the paper is a formulation of the results in terms of geometric objects on associated bundles over M rather than on bundles over P.

Publication Title

Journal of Geometry and Physics

Volume

6

Issue

1

First Page

107

Last Page

125

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