Publications and Preprints

A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. II : Supmech and Quantum Systems
Tulsi Dass
Supmech, which is noncommutative Hamiltonian mechanics (NHM) (developed in paper I) with two extra ingredients : positive observable valued measures (PObVMs) [which serve to connect state-induced expectation values and classical probabilities] and the `CC condition' [which stipulates that the sets of observables and pure states be mutually separating] is proposed as a universal mechanics aimed at covering all physical phenomena. Quantum systems, defined algebraically as supmech hamiltonian systems with non-supercommutative system algebras, are shown to inevitably have Hilbert space based realizations (so as to accommodate rigged Hilbet space based Dirac bra-ket formalism), generally admitting commutative superselection rules. Traditional features of quantum mechanics of finite particle systems appear naturally in an autonomous development. Treating massive particles as localizable elementary quantum systems, the Schr$\ddot{o}$dinger wave functions with traditional Born interpretation appear as natural objects for their description and the Schr$\ddot{o}$dinger equation for them is obtained without ever using a classical Hamiltonian or Lagrangian.

isid/ms/2010/01 [fulltext]

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