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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2012
1. Verfasser: Oeckl, R.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2012
Online Zugang: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
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-148384
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation
spellingShingle Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation
Oeckl, R.
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
author Oeckl, R.
author_facet Oeckl, R.
publishDate 2012
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
work_keys_str_mv AT oecklr holomorphicquantizationoflinearfieldtheoryinthegeneralboundaryformulation
first_indexed 2025-12-07T19:28:39Z
last_indexed 2025-12-07T19:28:39Z
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