Diffusion fields, quantum fields, and fields with values in Lie groups. (English) Zbl 0575.60078

Stochastic analysis and applications, Adv. Probab. Relat. Top. 7, 1-98 (1984).
[For the entire collection see Zbl 0541.00008.]
This is a review of topics related to quantum mechanics and quantum field theory. First, the authors discuss the theory of Dirichlet forms from its definition in sections 2 and 3. Then they review the results on two dimensional Euclidean field theory and discuss the global Markov property. At the end of section 4, they discuss the canonical structure of Markov Euclidean field. Finally, they review the results on the representation theory of Sobolev Lie groups of functions with values in compact simple Lie group. This article is easy to read even for non- experts and presents a lot of problems.
Reviewer: S.Kusuoka


60J60 Diffusion processes
81T08 Constructive quantum field theory
60G60 Random fields
60J99 Markov processes


Zbl 0541.00008