General Boundary Formulation for $n$-Dimensional Classical Abelian Theory with Corners

Symmetry Integrability and Geometry-Methods and Applications

article

Homero G. Díaz-Marín¹ 

[1] Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

关键词: gauge fields;    action;    manifolds with corners;   

DOI  :  10.3842/SIGMA.2015.048

来源: National Academy of Science of Ukraine

【 摘 要 】

We propose a general reduction procedure for classical field theories provided with abelian gauge symmetries in a Lagrangian setting. These ideas come from an axiomatic presentation of the general boundary formulation (GBF) of field theories, mostly inspired by topological quantum field theories (TQFT). We construct abelian Yang-Mills theories using this framework. We treat the case for space-time manifolds with smooth boundary components as well as the case of manifolds with corners. This treatment is the GBF analogue of extended TQFTs. The aim for developing this classical formalism is to accomplish, in a future work, geometric quantization at least for the abelian case.

【 授权许可】

Unknown