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 satisfied. 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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