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Q-adapted quantum stochastic integrals and differentials in Fock scale

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Belavkin V., Brown M.

Banach Center Publications

2011

tom 96

nr 1

51-66

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 $𝔉_𝕏$, 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.

Ograniczanie wyników

1 Banach Center Publications

1 Belavkin V.

1 Brown M.

1 2011

Wyniki wyszukiwania

Q-adapted quantum stochastic integrals and differentials in Fock scale