Mutual quadratic variation and ito's table in quantum stochastic calculus

Abstract

We discuss the relation between the mutual quadratic variation of two measures and the Ito table in quantum stochastic calculus. We prove the existence of the mutual quadratic variation of field- and gauge-measures in a quasi-free representation of the CCR in the topology of strong convergence on an appropriate invariant domain. We characterise the Fock state in terms of the mutual quadratic variation of the field-and gauge-measures. The higher order quadratic variations of these measures are computed in a general quasi-free representation.