Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the Kähler case, state spaces arise as spaces of holomorphic functions on linear spaces of classical solutions in...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148384 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation / R. Oeckl // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731840716013568 |
|---|---|
| author | Oeckl, R. |
| author_facet | Oeckl, R. |
| citation_txt | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation / R. Oeckl // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the Kähler case, state spaces arise as spaces of holomorphic functions on linear spaces of classical solutions in neighborhoods of hypersurfaces. Amplitudes arise as integrals of such functions over spaces of classical solutions in regions of spacetime. We prove the validity of the TQFT-type axioms of the general boundary formulation under reasonable assumptions. We also develop the notions of vacuum and coherent states in this framework. As a first application we quantize evanescent waves in Klein-Gordon theory.
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| first_indexed | 2025-12-07T19:28:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148384 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:28:39Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Oeckl, R. 2019-02-18T11:17:54Z 2019-02-18T11:17:54Z 2012 Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation / R. Oeckl // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 57R56; 81S10; 81T05; 81T20 DOI: http://dx.doi.org/10.3842/SIGMA.2012.050 https://nasplib.isofts.kiev.ua/handle/123456789/148384 We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the Kähler case, state spaces arise as spaces of holomorphic functions on linear spaces of classical solutions in neighborhoods of hypersurfaces. Amplitudes arise as integrals of such functions over spaces of classical solutions in regions of spacetime. We prove the validity of the TQFT-type axioms of the general boundary formulation under reasonable assumptions. We also develop the notions of vacuum and coherent states in this framework. As a first application we quantize evanescent waves in Klein-Gordon theory. I would like to thank Daniele Colosi for stimulating discussions. This work was supported in
 part by CONACyT grant 49093. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation Article published earlier |
| spellingShingle | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation Oeckl, R. |
| title | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation |
| title_full | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation |
| title_fullStr | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation |
| title_full_unstemmed | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation |
| title_short | Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation |
| title_sort | holomorphic quantization of linear field theory in the general boundary formulation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148384 |
| work_keys_str_mv | AT oecklr holomorphicquantizationoflinearfieldtheoryinthegeneralboundaryformulation |