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Quantum analysis—Non-commutative differential and integral calculi

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Abstract

A new scheme of quantum analysis, namely a non-commutative calculus of operator derivatives and integrals is introduced. This treats differentiation of an operator-valued function with respect to the relevant operator in a Banach space. In this new scheme, operator derivatives are expressed in terms of the relevant operator and its inner derivation explicitly. Derivatives of hyperoperators are also defined. Some possible applications of the present calculus to quantum statistical physics are briefly discussed.

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Authors and Affiliations

  1. Department of Physics, University of Tokyo, Bunkyo-ku, 113, Tokyo, Japan

    Masuo Suzuki

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  1. Masuo Suzuki
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Communicated by H. Araki

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Suzuki, M. Quantum analysis—Non-commutative differential and integral calculi. Commun.Math. Phys. 183, 339–363 (1997). https://doi.org/10.1007/BF02506410

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  • DOI: https://doi.org/10.1007/BF02506410

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