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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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148384 |
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irk-123456789-1483842019-02-19T01:23:32Z Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation Oeckl, R. 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148384 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Oeckl, R. |
| spellingShingle |
Oeckl, R. Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Oeckl, R. |
| author_sort |
Oeckl, R. |
| title |
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_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_sort |
holomorphic quantization of linear field theory in the general boundary formulation |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148384 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT oecklr holomorphicquantizationoflinearfieldtheoryinthegeneralboundaryformulation |
| first_indexed |
2023-05-20T17:30:37Z |
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2023-05-20T17:30:37Z |
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1796153463871111168 |