Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-02-25
Phys.Lett.B536:305-314,2002
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, LaTeX, typos corrected
Scientific paper
10.1016/S0370-2693(02)01865-8
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 of quantum mechanics, based on the Kahler structure of a complex projective Hilbert space, is recovered. We point out various novel features of this extended quantum mechanics, including its geometric aspects. Our approach sheds a new light on the problem of quantization of Nambu dynamics. Finally, we argue that the structure of this nonlinear quantum mechanics is natural from the point of view of string theory.
Minic Djordje
Tze Chia-Hsiung
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