Journal article
Reflection Positive Stochastic Processes Indexed by Lie Groups
Symmetry, integrability and geometry, methods and applications, Vol.12, 058
01/01/2016
DOI: 10.3842/SIGMA.2016.058
Abstract
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.
Details
- Title: Subtitle
- Reflection Positive Stochastic Processes Indexed by Lie Groups
- Creators
- Palle E. T Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAKarl-Hermann Neeb - FAU Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, GermanyGestur Olafsson - Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
- Resource Type
- Journal article
- Publication Details
- Symmetry, integrability and geometry, methods and applications, Vol.12, 058
- DOI
- 10.3842/SIGMA.2016.058
- ISSN
- 1815-0659
- eISSN
- 1815-0659
- Publisher
- NATL ACAD SCI UKRAINE, INST MATH
- Number of pages
- 49
- Language
- English
- Date published
- 01/01/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984241043902771
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