Quantum Feynman-Kac perturbations

Details Quantum Feynman-Kac perturbations Quantum Feynman-Kac perturbations

2012-02-29

arxiv.org/abs/1202.6489v1

Mathematics

Functional Analysis

25 pages

Scientific paper

We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. The multiplier cocycles are governed by quantum stochastic differential equations whose coefficients are driven by the unperturbed flow; under certain regularity conditions, we show that every multiplier cocycle is so described. Our results generalise those obtained using classical Brownian motion on the one hand, and results for unitarily implemented free flows on the other.

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