Locality and General Vacua in Quantum Field Theory
We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations, which occur generically on timelike hypersurfaces in Lorentzian spacetimes, as has been shown...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211350 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Locality and General Vacua in Quantum Field Theory. Daniele Colosi and Robert Oeckl. SIGMA 17 (2021), 073, 83 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748568663621632 |
|---|---|
| author | Colosi, Daniele Oeckl, Robert |
| author_facet | Colosi, Daniele Oeckl, Robert |
| citation_txt | Locality and General Vacua in Quantum Field Theory. Daniele Colosi and Robert Oeckl. SIGMA 17 (2021), 073, 83 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations, which occur generically on timelike hypersurfaces in Lorentzian spacetimes, as has been shown recently. We achieve this in two ways: On the one hand, we replace Hilbert space states by observables localized on hypersurfaces, in the spirit of algebraic quantum field theory. On the other hand, we apply the GNS construction to twisted star-structures to obtain Hilbert spaces, motivated by the notion of reflection positivity of the Euclidean approach to quantum field theory. As one consequence, the well-known representation of a vacuum state in terms of a sea of particle pairs in the Hilbert space of another vacuum admits a vast generalization to non-Kähler vacua, particularly relevant on timelike hypersurfaces.
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| first_indexed | 2026-04-17T19:51:07Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211350 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T19:51:07Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Colosi, Daniele Oeckl, Robert 2025-12-30T15:53:41Z 2021 Locality and General Vacua in Quantum Field Theory. Daniele Colosi and Robert Oeckl. SIGMA 17 (2021), 073, 83 pages 1815-0659 2020 Mathematics Subject Classification: 81P16; 81S10; 81S40; 81T20; 81T70 arXiv:2009.12342 https://nasplib.isofts.kiev.ua/handle/123456789/211350 https://doi.org/10.3842/SIGMA.2021.073 We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations, which occur generically on timelike hypersurfaces in Lorentzian spacetimes, as has been shown recently. We achieve this in two ways: On the one hand, we replace Hilbert space states by observables localized on hypersurfaces, in the spirit of algebraic quantum field theory. On the other hand, we apply the GNS construction to twisted star-structures to obtain Hilbert spaces, motivated by the notion of reflection positivity of the Euclidean approach to quantum field theory. As one consequence, the well-known representation of a vacuum state in terms of a sea of particle pairs in the Hilbert space of another vacuum admits a vast generalization to non-Kähler vacua, particularly relevant on timelike hypersurfaces. The authors would like to thank the anonymous referees for contributing to improving the clarity of exposition of the present article. This work was partially supported by CONACYT project grant 259258 and UNAM-PAPIIT project grant IA-106418. This publication was made possible through the support of the ID#61466 grant from the John Templeton Foundation, as part of the "Quantum Information Structure of Space time (QISS)" Project (qiss.fr). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Locality and General Vacua in Quantum Field Theory Article published earlier |
| spellingShingle | Locality and General Vacua in Quantum Field Theory Colosi, Daniele Oeckl, Robert |
| title | Locality and General Vacua in Quantum Field Theory |
| title_full | Locality and General Vacua in Quantum Field Theory |
| title_fullStr | Locality and General Vacua in Quantum Field Theory |
| title_full_unstemmed | Locality and General Vacua in Quantum Field Theory |
| title_short | Locality and General Vacua in Quantum Field Theory |
| title_sort | locality and general vacua in quantum field theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211350 |
| work_keys_str_mv | AT colosidaniele localityandgeneralvacuainquantumfieldtheory AT oecklrobert localityandgeneralvacuainquantumfieldtheory |