Q-adapted quantum stochastic integrals and differentials in Fock scale

Viacheslav Belavkin, and Matthew Brown. "Q-adapted quantum stochastic integrals and differentials in Fock scale." Banach Center Publications 96.1 (2011): 51-66. <http://eudml.org/doc/281905>.

@article{ViacheslavBelavkin2011,
abstract = {In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field $_$, of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone (Q = O) quantum dynamics. These may be of particular interest to quantum field theory, quantum open systems, and quantum theory of stochastic processes.},
author = {Viacheslav Belavkin, Matthew Brown},
journal = {Banach Center Publications},
keywords = {quantum stochastic calculus; non-adapted stochastic integrals; white noise analysis; Fock space calculus},
language = {eng},
number = {1},
pages = {51-66},
title = {Q-adapted quantum stochastic integrals and differentials in Fock scale},
url = {http://eudml.org/doc/281905},
volume = {96},
year = {2011},
}

TY - JOUR
AU - Viacheslav Belavkin
AU - Matthew Brown
TI - Q-adapted quantum stochastic integrals and differentials in Fock scale
JO - Banach Center Publications
PY - 2011
VL - 96
IS - 1
SP - 51
EP - 66
AB - In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field $_$, of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone (Q = O) quantum dynamics. These may be of particular interest to quantum field theory, quantum open systems, and quantum theory of stochastic processes.
LA - eng
KW - quantum stochastic calculus; non-adapted stochastic integrals; white noise analysis; Fock space calculus
UR - http://eudml.org/doc/281905
ER -