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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-3,
author = {Viacheslav Belavkin and Matthew Brown},
title = {Q-adapted quantum stochastic integrals and differentials in Fock scale},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {51-66},
zbl = {1261.81080},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-3}
}
Viacheslav Belavkin; Matthew Brown. Q-adapted quantum stochastic integrals and differentials in Fock scale. Banach Center Publications, Tome 95 (2011) pp. 51-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-3/