  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.
