Local symmetries in gauge theories in a finite-dimensional setting

Abstract

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization.

23 pages

References in corpus (2)

• The generally covariant locality principle -- A new paradigm for local quantum physics
• Covariant Poisson Brackets in Geometric Field Theory

Cited by in corpus (6)

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• Gauge reduction in covariant field theory