Theoretical Statistics and Mathematics Unit, ISI Delhi

Universality of quantum symplectic structure

by 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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