Nambu quantum mechanics: a nonlinear generalization of geometric quantum mechanics
نویسندگان
چکیده
منابع مشابه
Nambu Quantum Mechanics: A Nonlinear Generalization of Geometric Quantum Mechanics
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal evolution given by Jacobi elliptic functions. In the limit where latter’s moduli parameters are set to zero, the usual geometric formulation o...
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An extension of quantum mechanics to a generalized Nambu dynamics leads to a new version of nonlinear quantum mechanics. The time evolution of states is given in here by a triple bracket generalization of the Liouville-von Neumann equation, where one of the generators is an average energy, and the other is a measure of entropy. A nonlinear evolution can occur only for mixed states, and for syst...
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We present recent developments in the theory of Nambu mechanics, which include new examples of Nambu-Poisson manifolds with linear Nambu brackets and new representations of Nambu-Heisenberg commutation relations. Mathematics Subject Classification (1991) 70H99, 58F07
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Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of “mixed state” for any nonlinear version of quantum theory are introduced: (i) genuine mixture corresponds to operational “mixing” of different ensembles, and (ii) a mixture described by single density matrix without having a canonical operational possibility to pick out its specific convex decompos...
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In order to prevent “unavoidable” break-down of the “peaceful coexistence” between foundations of quantum theory and relativity I propose a new type of a quantum gauge theory (superrelativity). This differs from ordinary gauge theories in the sense that the affine connection of this theory is constructed from first derivatives of the Fubini-Study metric tensor in the projective Hilbert space of...
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ژورنال
عنوان ژورنال: Physics Letters B
سال: 2002
ISSN: 0370-2693
DOI: 10.1016/s0370-2693(02)01865-8