Abstract Markov property and local operators (Q1915346)

Generalized random fields with certain Markov properties are constructed. To unify the different approaches to the notions of Markov property, the author defines a general set-up, including different index sets, and a suitable Markov property called ``abstract'' Markov property. This set-up is formulated in the context of manifolds and bundle-sections. It is proved the preservation of the abstract Markov property for local operators on specific vector spaces. Under some assumptions on the index spaces involved the author discusses the preseparation of the \(c\)-Markov property. The illustrative examples are taken from quantum field theory. In the last section, the relation between different Markov properties is clarified.