Related papers: Quantum form of Nonlinear Maxwell Equation
In the context of the Feynman's derivation of electrodynamics, we show that noncommutativity allows other particle dynamics than the standard formalism of electrodynamics.
The quantum vacuum constitutes a fascinating medium of study, in particular since near-future laser facilities will be able to probe the nonlinear nature of this vacuum. There has been a large number of proposed tests of the low-energy,…
In electrodynamics courses and textbooks the properties of plane electromagnetic waves in both conducting and non-conducting media are typically studied from the point of view of the prototype case of a monochromatic plane wave. In this…
The aim of this paper is to formulate a {\it non--commutative geometrical} version of the classical electromagnetic field theory in the vacuum with the Moyal--Weyl algebra as the space--time by using the theory of quantum principal bundles…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude…
In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing…
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness when the density function is near the global Maxwellian and…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…