Markov structures on Clifford algebras

The minimal unitary dilations of contraction semigroups on Hilbert spaces naturally yield systems of orthogonal projections with pre-Markovian properties. Antisymmetric second quantization is a functorial construction on Hilbert space contractions which takes semigroups into doubly Markovian contraction semigroups on a scale of Banach spaces associated with certain Clifford algebras. Multiplicative functionals are introduced which are related to perturbations of these semigroups by a formula of the Feynman-Kac-Nelson type.