Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Quasi-free stochastic integral representation theorems over the CCR

Ivan F. Wildea1

a1 Department of Mathematics, King's College, Strand, London WC 2R 2LS


It is shown that each vector in the Hilbert space of certain quasi-free representations of the CCR can be written uniquely in terms of quantum stochastic integrals. As a consequence, we obtain general vector-valued and operator-valued boson quantum martingale representation theorems.

(Received December 14 1987)