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Reflection Positive Stochastic Processes Indexed by Lie Groups
Journal article   Open access   Peer reviewed

Reflection Positive Stochastic Processes Indexed by Lie Groups

Palle E. T Jorgensen, Karl-Hermann Neeb and Gestur Olafsson
Symmetry, integrability and geometry, methods and applications, Vol.12, 058
01/01/2016
DOI: 10.3842/SIGMA.2016.058
url
https://doi.org/10.3842/SIGMA.2016.058View
Published (Version of record) Open Access

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.
Physical Sciences Physics Physics, Mathematical Science & Technology

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