Fermion Ito's formula. II: The gauge process in fermion Fock space (Q1122887)

Summary: The stochastic calculus constructed by the author and \textit{R. L. Hudson} in Commun. Math. Phys. 96, 473-496 (1984; Zbl 0572.60052), for fermion Brownian motion is augmented through the inclusion of stochastic integration with respect to the gauge process. The solutions of certain non-commutative stochastic differential equations are used to construct dilations of contraction semigroups on a Hilbert space \({\mathfrak h}_ 0\) and of uniformly continuous, completely positive semigroups on B(\({\mathfrak h}_ 0)\). Finally we construct a fermion analogue of the classical Poisson process and investigate some of its properties.