Reflection Positive Stochastic Processes Indexed by Lie Groups

Symmetry Integrability and Geometry-Methods and Applications

article

Palle E.T. Jorgensen¹  Karl-Hermann Neeb²  Gestur Ólafsson³ 

[1] Department of Mathematics, The University of Iowa;Department Mathematik;Department of mathematics, Louisiana State University

关键词: reflection positivity;    stochastic process;    unitary representations;   

DOI  :  10.3842/SIGMA.2016.058

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown