Quantum Feynman-Kac perturbations

Belton, Alexander C. R. and Lindsay, J. Martin and Skalski, Adam G. (2014) Quantum Feynman-Kac perturbations. Journal of the London Mathematical Society, 89 (1). pp. 275-300. ISSN 1469-7750

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Abstract

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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the London Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
61853
Deposited By:
Deposited On:
24 Jan 2013 05:34
Refereed?:
Yes
Published?:
Published
Last Modified:
18 Nov 2020 11:53