Related papers: A realistic interpretation of the density matrix I…
The interpretation proposed in quant-ph/9812011 is extended to the general case of a non-relativistic particle moving in an arbitrary external potential. It is shown that, even in this general case, "particle" solutions exist which do not…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
Electrons in materials containing heavy elements are fundamentally relativistic and should in principle be described using the Dirac equation. However, the current standard for treatment of electrons in such materials involves density…
A concise discussion of the 3-dimensional irreducible (1,0) and (0,1) representations of the restricted Lorentz group and their application to the description of the electromagnetic field is given. It is shown that a mass term is in…
I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
A new notion of displacement convexity on a matrix level is developed for density flows arising from mean-field games, compressible Euler equations, entropic interpolation, and semi-classical limits of non-linear Schr\"odinger equations.…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
In this work a periodic crystal with point defects is described in the framework of linear response theory for broken symmetry states using correlation functions and Zwanzig-Mori equations. The main results are microscopic expressions for…
Several families of nonlinear field equations are known to possess space- localized singularity-free solutions which describe fields with finite Hermitian norms. This paper studies the interaction of such fields with given electromagnetic…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
We provide for the first time the exact solution of Maxwell's equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the…
Inspired by recent developments in electron chirality, we reconsider some microscopic physical quantities that have been overlooked or have received little attention in condensed matter physics, based on the non-relativistic limit of the…
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly its spectral decomposition. The…
A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified…
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac…
The paper shows the relationship between the major wave equations in quantum mechanics and electromagnetism, such as Schroedinger's equation, Dirac's equation and the Maxwell equations. It is shown that they can be derived in a striking…
We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework…