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On q-deformed quantum stochastic calculus

Piotr Sniady
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Abstract

In this paper we investigate a quantum stochastic calculus build of creation, annihilation and number of particles operators which fulfill some deformed commutation relations. Namely, we introduce a deformation of a number of particles operator which has simple commutation relations with well known q-deformed creation and annihilation operators. Since all operators considered in this theory are bounded we do not deal with some difficulties of a non deformed theory of Hudson and Parthasarathy. We define stochastic integrals and estimate them in the operator norm. We prove Ito's formula as well.

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Piotr Sniady. 2000-07-26. On q-deformed quantum stochastic calculus. https://arxiv.org/abs/math-ph/0007035

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