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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| Дата: | 2016 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147754 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147754 |
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dspace |
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irk-123456789-1477542019-02-16T01:24:20Z Reflection Positive Stochastic Processes Indexed by Lie Groups Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147754 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 |
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. |
| format |
Article |
| author |
Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. |
| spellingShingle |
Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. Reflection Positive Stochastic Processes Indexed by Lie Groups Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Jorgensen, P.E.T. Neeb, K.H. Ólafsson, G. |
| author_sort |
Jorgensen, P.E.T. |
| title |
Reflection Positive Stochastic Processes Indexed by Lie Groups |
| title_short |
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_sort |
reflection positive stochastic processes indexed by lie groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147754 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:28:13Z |
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2023-05-20T17:28:13Z |
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