Related papers: Complex-Distance Potential Theory and Hyperbolic E…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
Based on the classical limit of relativistic scattering amplitudes, we compute the coupling between a general super-renormalizable gravity and massive scalar particles. This allows us to derive the $D$-dimensional metric corrections at both…
To provide a unified theoretical framework ranging from a cellular-level excitation mechanism to organic-level geometric propagation, a new theory inspired by quantum electrodynamic theory for light propagation is proposed by describing the…
A theory of degenerate metrics is developed and applied to the problem of unifying gravitation with electromagnetism. The approach is similar to the Kaluza-Klein approach with a fifth dimension, however no ad hoc conditions are needed to…
In the wave equation obeyed by electromagnetic fields in curved spacetime there are Riemann and Ricci curvature coupling terms to the photon polarisation, which result in a polarisation dependent deviation of the photon trajectories from…
We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the experimental data of the $\rho$ meson spectrum. For this purpose we make use of the emergent bulk geometry obtained by deep learning from the…
The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the…
The presence of the term $\left(\case{v}{c}\right)$ that characterizes the electrodynamic retarded potentials, also known as Li\'enard-Wiechert potentials, is thought to be reminiscent of a Doppler effect. Here, we show that these…
In this paper we first make and discuss a conjecture concerning Newtonian potentials in Euclidean n space which have all their mass on the unit sphere about the origin, and are normalized to be one at the origin. The conjecture essentially…
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…
The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
The extension of the Dirac Delta distribution (DD) to the complex field is needed for dealing with the complex-energy solutions of the Schr\"odinger equation, typically when calculating their inner products. In quantum scattering theory the…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Chock Hypothesis, an explicit description of this influence is derived. We present a…
The proper time formalism for a particle propagator in an external electromagnetic field is combined with the path-dependent formulation of the gauge theory to simplify the quasiclassical propagator. The latter is achieved due to a specific…
This paper reports a numerical study of complex classical trajectories of a particle in an elliptic potential. This study of doubly-periodic potentials is a natural sequel to earlier work on complex classical trajectories in trigonometric…
We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling…
In a thermal field theory, the cumulants of the momentum distribution can be extracted from the dependence of the Euclidean path integral on a shift in the fields built into the temporal boundary condition. When combined with the Ward…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…