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The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Complete and physically adequate analytical and semi-analytical solutions have been obtained using a practical dimensionless form of kinetic equation assuming azimuthal symmetry and Maxwellian distributions of target plasma species.…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
It is well-known that the 5D gauge structure of Stueckelberg-Horwitz-Piron (SHP) electrodynamics permits the exchange of mass between particles and the fields induced by their motion, even at the classical level. This phenomenon presents…
In this paper we analyze again a transition from the classical to quantum description of bound charged particles, which involves a substantial modification of the structure of their electromagnetic (EM) fields related to the well-known fact…
We investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there…
This work builds on the following result of a previous article (quant-ph/0509044): the matter field can be naturally eliminated from the equations of the scalar electrodynamics (the Klein-Gordon-Maxwell electrodynamics) in the unitary…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…
If we study the quantum effects in plasmas in terms of traditional hydrodynamics via the continuity and Euler equations we find the quantum Bohm potential and the force of spin-spin interaction. However, if we extend the set hydrodynamic…
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form.…
We present a classical and quantum analysis of a particle confined in a three-dimensional paraboloidal cavity formed by two confocal paraboloids. Classically, the system is integrable and presents three independent constants of motion,…
In an earlier paper we provided an alternative to the standard gauge concept for deriving the classical electromagnetic wave equations. This alternative involves recognition of two previously overlooked basic equations and represents a…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems…
The interplay between off-shell and on-shell unfolded systems is analysed. The formulation of invariant constraints that put an off-shell system on shell is developed by adding new variables and derivation in the target space, that extends…
We show that quantum mechanics can be constructed as a classical field theory that correctly describes all basic quantum effects. We construct the self-consistent Maxwell-Pauli theory, from which the correct spontaneous emission spectrum of…
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the…