Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale
Mathematical Physics
2011-12-02 v1 Information Theory
math.IT
math.MP
Quantum Algebra
Quantum Physics
Abstract
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS integration over a space-time. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative is proved. Finally, Q-adapted dynamics is discussed, including Bosonic Q=1, Fermionic Q=-1, and monotone Q=0 quantum dynamics. These may be of particular interest to quantum field theory, quantum open systems, and quantum theory of stochastic processes.
Cite
@article{arxiv.1112.0147,
title = {Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale},
author = {Viacheslav P. Belavkin and Matthew F. Brown},
journal= {arXiv preprint arXiv:1112.0147},
year = {2011}
}
Comments
A similar version is due to appear in the proceedings of the 13th workshop: non-commutative harmonic analysis. 18 pages