The gauge invariant relativistic quantum equations of motion for the fermion and photon Wigner operators are derived from QED. In the mean field (Hartree) approximation, we extract the generalized quantum Vlasov and mass-shell constraint equations for fermions. In addition, a complete spinor decomposition is performed. A systematic method for computing quantum corrections to all orders in Ii is developed. First order quantum (spin) corrections are computed explicitly. Finally, the relations between gauge dependent and independent definitions of the photon Wigner function and their corresponding transport equations are discussed.

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A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and may be relevant for the foundations of quantum mechanics, in particular, when it comes to experiments exploring the quantum-classical border. The present linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fullfill all consistency requirements discussed in the literature, while earlier attempts failed in this respect. Our work is based on the representation of quantum mechanics in the framework of classical analytical mechanics by A. Heslot, showing that notions of states in phase space, observables, Poisson brackets, and related canonical transformations can be naturally extended to quantum mechanics. This is suitably generalized for quantum-classical hybrids here.Comment: Replaced by final revtex version; references updated, section V.E. adde

We study a classical reparametrization-invariant system, in which "time" is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a suitable potential, the internal motion is ergodic or more strongly irregular. We consider quasi-local observables which measure the system's "change" in a coarse-grained way. Based on this, we construct a statistical timelike parameter, particularly with the help of maximum entropy method and FisherRao information metric. The emergent reparametrization-invariant "time" does not run smoothly but is simply related to the proper time on the average. For sufficiently low energy, the external motion is then described by a unitary quantum mechanical evolution in accordance with the Schrödinger equation.

We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for a set of bandwidth limited harmonic oscillators, which encode the Schrödinger equation. Thus, the linearity of quantum mechanics is related to the action principle of such cellular automata and its conservation laws to discrete ones.

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We study the reparametrization invariant system of a classical relativistic particle moving in (5+1) dimensions, of which two internal ones are compactified to form a torus. A discrete physical time is constructed based on a quasi-local invariant observable. Due to ergodicity, it is simply related to the proper time on average. The external motion in Minkowski space can then be described as a unitary quantum mechanical evolution.