Reflection Positive Stochastic Processes Indexed by Lie Groups
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symme...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147754 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Reflection Positive Stochastic Processes Indexed by Lie Groups / P.E.T. Jorgensen, K.H. Neeb, G. Ólafsson // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 68 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862630607608086528 |
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| author | Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. |
| author_facet | Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. |
| citation_txt | Reflection Positive Stochastic Processes Indexed by Lie Groups / P.E.T. Jorgensen, K.H. Neeb, G. Ólafsson // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 68 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations.
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| first_indexed | 2025-11-30T10:12:39Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147754 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T10:12:39Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. 2019-02-15T19:11:21Z 2019-02-15T19:11:21Z 2016 Reflection Positive Stochastic Processes Indexed by Lie Groups / P.E.T. Jorgensen, K.H. Neeb, G. Ólafsson // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 68 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 22E45; 60G15; 81S40 DOI:10.3842/SIGMA.2016.058 https://nasplib.isofts.kiev.ua/handle/123456789/147754 Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations. The research of P. Jorgensen was partially supported by the Binational Science Foundation
 Grant number 2010117. The research of K.-H. Neeb was supported by DFG-grant NE 413/7-2,
 Schwerpunktprogramm “Darstellungstheorie”. The research of G. Olafsson was supported by ´
 NSF grant DMS-1101337. The authors wish to thank the Mathematisches Forschungsinstitut
 Oberwolfach for hosting a Workshop on “Reflection Positivity in Representation Theory,
 Stochastics and Physics” November, 30 – December 6, 2014. The present research was started
 at the workshop, and it has benefitted from our discussions with the participants there. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Reflection Positive Stochastic Processes Indexed by Lie Groups Article published earlier |
| spellingShingle | Reflection Positive Stochastic Processes Indexed by Lie Groups Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. |
| title | Reflection Positive Stochastic Processes Indexed by Lie Groups |
| title_full | Reflection Positive Stochastic Processes Indexed by Lie Groups |
| title_fullStr | Reflection Positive Stochastic Processes Indexed by Lie Groups |
| title_full_unstemmed | Reflection Positive Stochastic Processes Indexed by Lie Groups |
| title_short | Reflection Positive Stochastic Processes Indexed by Lie Groups |
| title_sort | reflection positive stochastic processes indexed by lie groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147754 |
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