PUB - Publikationen an der Universität Bielefeld

We consider a model describing the coupling of a vector-valued and a scalar homogeneous Markovian random field over R-4, interpreted as expressing the interaction between a charged scalar quantum field coupled with a nonlinear quantized electromagnetic field. Expectations of functionals of the random fields are expressed by Brownian bridges. Using this, together with Feynman-Kac-Ito type formulae and estimates on the small time and large time behaviour of Brownian functionals, we prove asymptotic upper and lower bounds on the kernel of the transition semigroup for our model. The upper bound gives faster than exponential decay for large distances of the corresponding resolvent (propagator). Published by AIP Publishing.