Path Integrals on Euclidean Space Forms

In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, base...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2015
Main Authors: Capobianco, G., Reartes, W.
Format: Article
Language:English
Published: Інститут математики НАН України 2015
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147139
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Path Integrals on Euclidean Space Forms / G. Capobianco, W. Reartes // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 35 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862669436079570944
author Capobianco, G.
Reartes, W.
author_facet Capobianco, G.
Reartes, W.
citation_txt Path Integrals on Euclidean Space Forms / G. Capobianco, W. Reartes // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 35 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed. In the Rⁿ case the obtained results coincide with the known expressions.
first_indexed 2025-12-07T15:28:24Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-147139
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T15:28:24Z
publishDate 2015
publisher Інститут математики НАН України
record_format dspace
spelling Capobianco, G.
Reartes, W.
2019-02-13T17:24:11Z
2019-02-13T17:24:11Z
2015
Path Integrals on Euclidean Space Forms / G. Capobianco, W. Reartes // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 35 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 53Z05; 81S40
DOI:10.3842/SIGMA.2015.071
https://nasplib.isofts.kiev.ua/handle/123456789/147139
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed. In the Rⁿ case the obtained results coincide with the known expressions.
We thank Hern´an Cendra for his reading of the manuscript and useful suggestions. This work
 was supported by the Universidad Nacional del Sur (Grants PGI 24/L085, PGI 24/L086 and
 PGI 24/ZL10).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Path Integrals on Euclidean Space Forms
Article
published earlier
spellingShingle Path Integrals on Euclidean Space Forms
Capobianco, G.
Reartes, W.
title Path Integrals on Euclidean Space Forms
title_full Path Integrals on Euclidean Space Forms
title_fullStr Path Integrals on Euclidean Space Forms
title_full_unstemmed Path Integrals on Euclidean Space Forms
title_short Path Integrals on Euclidean Space Forms
title_sort path integrals on euclidean space forms
url https://nasplib.isofts.kiev.ua/handle/123456789/147139
work_keys_str_mv AT capobiancog pathintegralsoneuclideanspaceforms
AT reartesw pathintegralsoneuclideanspaceforms