TY - JOUR

T1 - Causal structure of quantum stochastic integrators

AU - Gough, J.

N1 - Funding Information:
This paper was partially written while the author was visiting the Centro Volterra Institute (Universits di Roma, Tor Vergata) under Italian Ministry of Foreign Affairs Fellowship No. 20924/95. I wish to thank Prof. L. Accardi for the warm hospitality afforded to me during this time. I would also like to thank Prof. I. Volovich for many stinmlating discussions on the subject of quantum noise and for introducing me to his own formalism for treating the Accardi, Frigerio, and Lu theory. I further wish to thank Prof. O. G. Smolianov (Moscow) and Prof. A. O'Farrell (Maynooth) for their helpful remarks during the writing of this paper.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1997/5

Y1 - 1997/5

N2 - A class of concrete representations of a noncommutative Stratonovich calculus is defined and its relation-ship with the quantum Itô calculus of Hudson and Parthasarathy is made explicit. Given a quantum field interacting with a quantum mechanical system, it is possible to extract a quantum noise description for the field using a suitable scaling limit (here, the weak coupling limit). The motivation for our construction is to discuss the relationship between the micro-causality of a quantum field and the notion of macro-causality of the quantum noise which replaces it. We derive the Stratonovich quantum stochastic differential equation for the limit evolution operator and show that it agrees with the quantum stochastic limit theory of Accardi, Frigerio, and Lu when we convert to the Itô form. The Stratonovich approach, being inherently closer to the physical microscopic equations, leads to an overwhelmingly simplified derivation of the quantum stochastic limit equations of motion. The unification of the two quantum stochastic calculi is given and their physical origins explained.

AB - A class of concrete representations of a noncommutative Stratonovich calculus is defined and its relation-ship with the quantum Itô calculus of Hudson and Parthasarathy is made explicit. Given a quantum field interacting with a quantum mechanical system, it is possible to extract a quantum noise description for the field using a suitable scaling limit (here, the weak coupling limit). The motivation for our construction is to discuss the relationship between the micro-causality of a quantum field and the notion of macro-causality of the quantum noise which replaces it. We derive the Stratonovich quantum stochastic differential equation for the limit evolution operator and show that it agrees with the quantum stochastic limit theory of Accardi, Frigerio, and Lu when we convert to the Itô form. The Stratonovich approach, being inherently closer to the physical microscopic equations, leads to an overwhelmingly simplified derivation of the quantum stochastic limit equations of motion. The unification of the two quantum stochastic calculi is given and their physical origins explained.

UR - http://www.scopus.com/inward/record.url?scp=0031526680&partnerID=8YFLogxK

U2 - 10.1007/BF02634267

DO - 10.1007/BF02634267

M3 - Article

AN - SCOPUS:0031526680

SN - 0040-5779

VL - 111

SP - 563

EP - 575

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

IS - 2

ER -