Euclidean quantum mechanics and stochastic integrals

by R. F. Streater; pp 371-393 in "Stochastic Integrals", ed. D. Williams, Lecture Nores in Mathematics, 851, Springer-Verlag. ISBN 3-540-10690-1.

ABSTRACT

We rewrite elementary quantum mechanics as a euclidean field theory, and find the analogues of the Wightman and Osterwalder-Schrader axioms. In the presence of an external magnetic field, the Feynman-Kac formula involved a stochastic integral, of the Stratonovitch type. If the external field is non-abelian, then the Feynman-Kac factor becomes a stochastic integral with non-commuting noise-a quantum stochastic integral.