Generalized quantum dynamics as pre-quantum mechanics

Generalized Quantum Dynamics as Pre-Quantum Mechanics

We address the issue of when generalized quantum dynamics, which is a classical symplectic dynamics for noncommuting operator phase space variables based on a graded total trace Hamiltonian H, reduces to Heisenberg picture complex quantum mechanics. We begin by showing that when H = TrH , with H a Weyl ordered operator Hamiltonian, then the generalized quantum dynamics operator equations of mot...

The Quantum Double as Quantum Mechanics

We introduce ∗-structures on braided groups and braided matrices. Using this, we show that the quantum double D(Uq(su2)) can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski space (a three-sphere in the Lorentz metric), and with the role of angular momentum played by Uq(su2). This provides a new example of a quantum system whose algebr...

Quantum Mechanics as Quantum Information, Mostly

In this paper, I try to cause some good-natured trouble. The issue is, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appear...

Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation

We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle. It is ...

Statistical Dynamics of Global Unitary Invariant Matrix Models as Pre-Quantum Mechanics