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Indian Journal of Pure and Applied Mathematics

Contributions of K. R. Parthasarathy (KRP) to Mathematics of Quantum theory - Perturbations of Operators and Quantum Stochastic Calculus

Kalyan B. Sinha

Published Jul 29, 2024• 0 citations
Publisher
DOI
10.1007/s13226-024-00658-5

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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.