Physics – Quantum Physics
Scientific paper
2002-07-18
Physics
Quantum Physics
44 pages
Scientific paper
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as the basic feature of quantum theory. Arguments are given to show that when such a unification is attempted at the configuration space level, the wave funtions of Schr$\ddot{o}$dinger theory appear as the natural candidates for the desired unification. A *-algebra $\mathcal{A}_{Q}$ of (not necessarily bounded) linear operators acting on an appropriate dense set of these wave functions appears as the arena for quantum kinematics. A simple generalization of an existing formalism in noncommutative geometry is employed to develop the notion of generalized algebraic symplectic structure (GASS) which can accomodate classical and quantum symplectic structures as special cases. Quantum kinematics and dynamics is developed in in the framework of a noncommutative Hamiltonian system employing an appropriate GASS based in $ \mathcal{A}_{Q}$. The Planck constant is introduced at only one place -- in the quantum symplectic form; its appearance at conventional places is then automatic. Unitary Wigner symmetries appear as canonical transformations in the noncommutative Hamiltonian system. A straightforward treatment of quantum - classical correspondence is given in terms of appropriate GASSes.
No associations
LandOfFree
Towards an Autonomous Formalism for Quantum Mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Towards an Autonomous Formalism for Quantum Mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Towards an Autonomous Formalism for Quantum Mechanics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-209940