arXiv 1202.64892012-02math.FAmath-phmath.MPmath.OAmath.PR

Quantum Feynman-Kac perturbations

Alexander C. R. Belton, J. Martin Lindsay, Adam G. Skalski

备注：: 27 pages. Minor corrections to version 2. To appear in the Journal of the London Mathematical Society
DOI：: 10.1112/jlms/jdt048

英文摘要：

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 characterised under alternative assumptions of separability or Markov regularity. Our results generalise those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.

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