Publications and Preprints

Universality of quantum symplectic structure
Tulsi Dass
Operating in the framework of `supmech'( a scheme of mechanics which aims at providing a concrete setting for the axiomatization of physics and of probability theory as required in Hilbert's sixth problem; integrating noncommutative symplectic geometry and noncommutative probability in an algebraic setting, it associates, with every `experimentally accessible' system, a symplectic algebra and operates essentially as noncommutative Hamiltonian mechanics with some extra sophistication in the treatment of states) it is shown that interaction between systems can be consistently described only if either (i) all system algebras are commutative or (ii) all system algebras are noncommutative and have a quantum symplectic structure characterized by a \emph{universal} Planck type real-valued constant of the dimension of action.

isid/ms/2007/10 [fulltext]

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