Quantum Feynman–Kac perturbations

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. Multiplier cocycles are constructed via quantum stochastic differential equati...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2014-02, Vol.89 (1), p.275-300
Main Authors: Belton, Alexander C. R., Lindsay, J. Martin, Skalski, Adam G.
Format: Article
Language:English
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Summary: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. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting class of cocycles is characterized under alternative assumptions of separability or Markov regularity. Our results generalize those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jdt048