Local symmetries in gauge theories in a finite-dimensional setting

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Forger, Michael¹  Soares, Bruno Learth¹ 

[1] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat Aplicada, BR-05315970 Sao Paulo, Brazil

关键词: Gauge theories;    Lie group bundles;    Global symmetries;    Local symmetries;   

DOI  :  10.1016/j.geomphys.2012.05.003

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free