Reflection positive stochastic processes indexed by Lie groups

Jorgensen PE, Neeb KH, Olafsson G (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Symmetry Integrability and Geometry-Methods and Applications National Academy of Science of Ukraine

Book Volume: 12

Journal Issue: 058

URI: https://arxiv.org/abs/1510.07445

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.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

University of Iowa US United States (USA) (US) Louisiana State University US United States (USA) (US)

How to cite

APA:

Jorgensen, P.E., Neeb, K.H., & Olafsson, G. (2016). Reflection positive stochastic processes indexed by Lie groups. Symmetry Integrability and Geometry-Methods and Applications, 12(058). https://doi.org/10.3842/SIGMA.2016.058

MLA:

Jorgensen, Palle E.T., Karl Hermann Neeb, and Gestur Olafsson. "Reflection positive stochastic processes indexed by Lie groups." Symmetry Integrability and Geometry-Methods and Applications 12.058 (2016).

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