Quantum Feynman-Kac perturbations
Functional Analysis
2018-01-18 v3 Mathematical Physics
math.MP
Operator Algebras
Probability
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.
Keywords
Cite
@article{arxiv.1202.6489,
title = {Quantum Feynman-Kac perturbations},
author = {Alexander C. R. Belton and J. Martin Lindsay and Adam G. Skalski},
journal= {arXiv preprint arXiv:1202.6489},
year = {2018}
}
Comments
27 pages. Minor corrections to version 2. To appear in the Journal of the London Mathematical Society