Publications and Preprints
A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. II : Supmech and Quantum Systems
by
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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