Local symmetries in gauge theories in a finite-dimensional setting

Details Local symmetries in gauge theories in a finite-dimensional setting Local symmetries in gauge theories in a finite-dimensional setting

2009-01-12

arxiv.org/abs/0901.1636v1

Physics

Mathematical Physics

23 pages

Scientific paper

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.

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