Constructive Approach to the Global Markov Property in Euclidean Quantum Field Theory I. Construction of Transition Kernels

#### S. Albeverio, R. Gielerak, F. Russo

1997, v.3, Issue 3, 275-322

ABSTRACT

The trace properties of the sample paths of sufficiently regular generalised random fields are studied. In particular, nice localisation properties are shown in the case of hyperplanes. Using techniques of Euclidean quantum field theory a constructive description of the conditional expectation values with respect to some Gibbs measures describing Euclidean quantum field theory models and the $\sigma$-algebras localised in half-spaces is given. In particular the global Markov property with respect to hyperplanes follows from these constructions in an explicit way.

Keywords: quantum field theory,global Markov property,Gibbsian perturbation of the free field