# Q-adapted quantum stochastic integrals and differentials in Fock scale

Viacheslav Belavkin; Matthew Brown

Banach Center Publications (2011)

- Volume: 96, Issue: 1, page 51-66
- ISSN: 0137-6934

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topViacheslav 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 -

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