Lie groupoids in classical field theory II: Gauge theories, minimal coupling and Utiyama's theorem

JOURNAL OF GEOMETRY AND PHYSICS

卷:169

Article

Costa, Bruno T.²  Forger, Michael¹  Pegas, Luiz Henrique P.³ 

[1] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo, SP, Brazil

[2] Univ Fed Santa Catarina, Dept Matemat, Rua Joao Pessoa 2750, BR-89036256 Blumenau, SC, Brazil

[3] Univ Fed Parana, Dept Matemat, Caixa Postal 19081, BR-81531980 Curitiba, Parana, Brazil

关键词: Lie groupoid;    Lie algebroid;    Symmetries;    Gauge theory;    Minimal coupling;    Utiyama's theorem;   

DOI  :  10.1016/j.geomphys.2021.104340

来源: Elsevier

【 摘 要 】

In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. In this second part, we shall adapt the formalism developed in the first paper to the context of gauge theories and deal with minimal coupling and Utiyama's theorem. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free