  A noncommutative Kunita-Watanabe-type representation theorem is established
for the martingales of quasifree states of CCR algebras. To this end the basic
theory of quasifree stochastic integrals is developed using the abstract It\^o
integral in symmetric Fock space, whose interaction with the operators of
Tomita-Takesaki theory we describe. Our results extend earlier quasifree
martingale representation theorems in two ways: the states are no longer
assumed to be gauge-invariant, and the multiplicity space may now be
infinite-dimensional. The former involves systematic exploitation of Araki's
Duality Theorem. The latter requires the development of a transpose on matrices
of unbounded operators, defying the lack of complete boundedness of the
transpose operation.
