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Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…
Various procedures for expressing the multipolar expansion of the electromagnetic field are considered with application to the calculation of the radiated power. Some results from literature are discussed and perspective of developing the…
A rigorous, modern version of Boole's algebra of logic is presented, based partly on the 1890s treatment of Ernst Schroder.
We present an explicit construction of a unitary representation of the commutator algebra satisfied by position and momentum operators on the Moyal plane.
We give a simple derivation and explanation of a recently proposed new relativistic interaction between the electron and the angular momentum of the electromagnetic field in quantum electrodynamics (QED). Our derivation is based on the work…
This article reviews recent work on the Kac master equation and its low dimensional counterpart, the Kac equation.
A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.
We consider non-linear elliptic equations having a measure in the right hand side, of the type $ \divo a(x,Du)=\mu, $ and prove differentiability and integrability results for solutions. New estimates in Marcinkiewicz spaces are also given,…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
Twisted K-theory has received much attention recently in both mathematics and physics. We describe some models of twisted K-theory, both topological and geometric. Then we state a theorem which relates representations of loop groups to…
F. Rohrlich has recently published two papers, including the paper under review, advocating a particular delay-differential equation as an approximate equation of motion for classical charged particles, which he characterizes as providing a…
We introduce a class of non-Moufang loops satisfying the Moufang's theorem.
This is a response to the comment by J. Lidmar on our work in Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622. We show explicitly that, contrary to the statements in the comment, our scaling analysis correctly reproduces the Josephson…
This work, that is devoted to the memory of Dr. Andrew Chubykalo and his legacy, is the improved version of the paper published in Annales de la Fondation Louis de Broglie journal. In this article, methods for solving the Maxwell equations…
We survey the classical results of the Dirichlet Approximation Theorem.
An equation of motion formalism for excited states in variational Monte Carlo is derived and a pilot implementation for the Jastrow-modified antisymmetric geminal power is tested. In single excitations across a range of small molecules,…
We derive the expressions for canonical energy, momentum, and angular momentum for multiple metric theories. We prove that although the metric fields are generally interacting, the total energy is the sum of conserved energies corresponding…