General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners
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 (TQ...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2015 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147116 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862576140744392704 |
|---|---|
| author | Díaz-Marín, H.G. |
| author_facet | Díaz-Marín, H.G. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-26T14:35:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147116 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T14:35:25Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Díaz-Marín, H.G. 2019-02-13T16:56:24Z 2019-02-13T16:56:24Z 2015 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. 1815-0659 2010 Mathematics Subject Classification: 53D30; 58E15; 58E30; 81T13 DOI:10.3842/SIGMA.2015.048 https://nasplib.isofts.kiev.ua/handle/123456789/147116 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners Article published earlier |
| spellingShingle | General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners Díaz-Marín, H.G. |
| title | General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners |
| title_full | General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners |
| title_fullStr | General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners |
| title_full_unstemmed | General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners |
| title_short | General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners |
| title_sort | general boundary formulation for n-dimensional classical abelian theory with corners |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147116 |
| work_keys_str_mv | AT diazmarinhg generalboundaryformulationforndimensionalclassicalabeliantheorywithcorners |