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General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners
Інший ID:
2010 Mathematics Subject Classification: 53D30; 58E15; 58E30; 81T13
DOI:10.3842/SIGMA.2015.048
DOI:10.3842/SIGMA.2015.048
Посилання:
General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners / H.G. Díaz-Marín // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 28 назв. — англ.
Підтримка:
The author thanks R. Oeckl for several discussions and encouragement for writing this note at
CCM-UNAM. This work was partially supported through a CONACYT-M´exico postdoctoral
grant. The author also thanks the referees for their comments and suggestions.
Дата:
2015
Переглядів:
568
Завантажень:
246
Анотація:
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.
