Related papers: Hilbert Space Theory of Classical Electrodynamics
The well known argument of Page and Wootters demonstrates how to "derive" the usual quantum dynamics of a subsystem in a global state which is an eigenstate of the total Hamiltonian. I show how the same argument can be made in classical…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion coefficients addressed in the literature are…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
We present a model of interacting quantum fields, formulated in a non-perturbative manner. One of the fields is treated semi-classically, the other is the photon field. The model has an interpretation of an electromagnetic field in a…
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…
We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projections of realistic dynamics in a ``prespace''. The basic…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
(abridged)If the space-time is presupposed, the coordinate representation of the solutions $\psi(\vec x, t)$ of the Schroedinger equation of a quantum system containing one massive scalar particle has a {\it preferred status}. It is then…
We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum…
Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates reconsidering the Hamiltonian formulation of…
The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the…