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Quantum dissipative systems. III. Definition and algebraic structure

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Abstract

Starting from the requirement of a consistent quantum description of dissipative (non-Hamiltonian) systems, which is formulated as the absence of a contradiction between the evolution equations for quantum dissipative systems and quantum commutation relations, we show that the Jacobi identity is not satisifed. Thus, the requirement for a consistent quantum description forces one go beyond the Lie algebra. As a result, anticommutative non-Lie algebras are necessary to describe dissipative (non-Hamiltonian) systems in quantum theory.

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Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, USSR

    V. E. Tarasov

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  1. V. E. Tarasov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 73–85, January, 1997.

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Tarasov, V.E. Quantum dissipative systems. III. Definition and algebraic structure. Theor Math Phys 110, 57–67 (1997). https://doi.org/10.1007/BF02630369

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