Continuous kernel processes in quantum probability - Waldenfels, Wilhelm von (Quantum probability communications, 2003)
We present in this paper a theory of quantum stochastic processes based on the notion of kernels, a notion well established in quantum field theory and introduced to quantum probability by H. Maassen. As we restrict ourselves to continuous kernel processes we shall need only the tools of classical calculus and the proofs become rather easy. For the solution of a linear quantum stochatic differential equation an explicit formula is obtained. Under the usual conditions the solution can be extended to a strongly continuous unitary cocycle. It is indicated how the white noise equation can be obtained as a limit of the coloured noise equation.
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