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Quantum Feynman-Kac perturbations

Research output: Contribution to journalJournal article

Published

Journal publication date02/2014
JournalJournal of the London Mathematical Society
Journal number1
Volume89
Number of pages26
Pages275-300
Early online date30/10/13
Original languageEnglish

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.