Related papers: Dirac lattices, zero-range potentials and self adj…
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…
One important development in interaction potential models, or atomistic force fields, for molecular simulation is the inclusion of explicit polarisation, which represents the induction effects of charged or polar molecules on polarisable…
A qubit lattice algorithm (QLA) is developed for Maxwell equations in a two-dimensional Cartesian geometry. In particular, the initial value problem of electromagnetic pulse scattering off a localized 2D dielectric object is considered. A…
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
We analyze one-dimensional photonic superlattices which alternate layers of air and a left-handed material. We assume Drude-type dispersive responses for the dielectric permittivity and magnetic permeability of the left-handed material.…
We contemplate the pair of the purely imaginary delta-function potentials on a finite interval with Dirichlet boundary conditions. The two parameter model exhibits nicely the expected quantitative features of the unavoided level crossing…
We study the full Maxwell-Dirac equations: Dirac field with minimally coupled electromagnetic field and Maxwell field with Dirac current as source. Our particular interest is the static case in which the Dirac current is purely time-like --…
We study Dirac field equations coupled to electrodynamics with metric and torsion fields: we discuss how special spinorial solutions are incompatible with torsion; eventually these results will be used to sketch a discussion on the problem…
The Planck length is the minimum length which physical law do not fail. The Dirac delta function was created to deal with continuous range issue, and it is zero except for one point. Thus contradict the Planck length. Renormalization method…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regu-larised vacuum energy. The leading order of this expansion is given by a classical formula due to…
We analyze mass renormalization in massive Dirac-like systems in (2+1) dimensions arising from electron-phonon interactions at finite temperatures, employing the large-$N$ expansion. Our model combines the low-energy description of charge…
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $\mathcal{C}^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the Dirac…
The dielectric nature of polar liquids underpins much of their ability to act as useful solvents, but its description is complicated by the long-ranged nature of dipolar interactions. This is particularly pronounced under the periodic…
We present a dual representation of the partition function of the charged scalar field in which the complex action problem at non-zero chemical potential is absent. In this dual representation Monte Carlo simulations are possible and we…
Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for…
The quasistatic field around a circular hole in a two-dimensional hyperbolic medium is studied. As the loss parameter goes to zero, it is found that the electric field diverges along four lines each tangent to the hole. In this limit, the…
This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…
The phase transition of the electroweak vacuum induced by a strong magnetic field is examined, and a connection is made with the Ginzburg-Landau theory of type-II superconductivity. For solutions of the exact nonlinear field equations of…
Given a bounded smooth domain $\Omega\subset\mathbb{R}^3$, we explore the relation between couplings of the free Dirac operator $-i\alpha\cdot\nabla+m\beta$ with pure electrostatic shell potentials $\lambda\delta_{\partial\Omega}$…