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Quantum Feynman-Kac perturbations

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Quantum Feynman-Kac perturbations. / Belton, Alexander C. R.; Lindsay, J. Martin; Skalski, Adam G.

In: Journal of the London Mathematical Society, Vol. 89, No. 1, 02.2014, p. 275-300.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Belton, ACR, Lindsay, JM & Skalski, AG 2014, 'Quantum Feynman-Kac perturbations', Journal of the London Mathematical Society, vol. 89, no. 1, pp. 275-300. https://doi.org/10.1112/jlms/jdt048

APA

Vancouver

Belton ACR, Lindsay JM, Skalski AG. Quantum Feynman-Kac perturbations. Journal of the London Mathematical Society. 2014 Feb;89(1):275-300. https://doi.org/10.1112/jlms/jdt048

Author

Belton, Alexander C. R. ; Lindsay, J. Martin ; Skalski, Adam G. / Quantum Feynman-Kac perturbations. In: Journal of the London Mathematical Society. 2014 ; Vol. 89, No. 1. pp. 275-300.

Bibtex

@article{e45bc26e05244e6296576a53f4b01ab4,
title = "Quantum Feynman-Kac perturbations",
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.",
author = "Belton, {Alexander C. R.} and Lindsay, {J. Martin} and Skalski, {Adam G.}",
year = "2014",
month = feb,
doi = "10.1112/jlms/jdt048",
language = "English",
volume = "89",
pages = "275--300",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Quantum Feynman-Kac perturbations

AU - Belton, Alexander C. R.

AU - Lindsay, J. Martin

AU - Skalski, Adam G.

PY - 2014/2

Y1 - 2014/2

N2 - 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.

AB - 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.

U2 - 10.1112/jlms/jdt048

DO - 10.1112/jlms/jdt048

M3 - Journal article

VL - 89

SP - 275

EP - 300

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 1

ER -