Related papers: Countable basis for free electromagnetic fields
A boundary integral formulation of electromagnetics that involves only the components of $\boldsymbol{E}$ and $\boldsymbol{H}$ is derived without the use of surface currents that appear in the classical PMCHWT formulation. The kernels of…
Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis…
This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space of a given dimension
We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting' for…
The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define…
In this paper, we explore the existence of various non-singular compact stellar solutions influenced by the Maxwell field within the matter-geometry coupling based modified gravity. We start this analysis by considering a static spherically…
The worldvolume theory of membrane is mathematically equivalent to three-dimensional quantum gravity coupled to matter fields corresponding to the target space coordinates of embedded membrane. In a recent paper [arXiv:1503.08812] a new…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
In this paper, we introduce an alternative representation of the electromagnetic field scattered from a homogeneous sphere coated with a homogeneous layer of uniform thickness. Specifically, we expand the scattered field using a set of…
We construct an example of a smooth, non analytic planar vector field with an {\omega}-limit set consisting of a countable number of homoclinic loops.
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…
Photodetection converts optical quantum states into measurement events, but the usual electric-field response model becomes restrictive when the detector response is shaped by cavity, superconducting, or metamaterial engineering. We develop…
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…
This paper aims to present the pure field part of the newly developed nonlinear {\it Extended Electrodynamics} [1]-[3] in non-relativistic terms, i.e. in terms of the electric and magnetic vector fields (${\mathbf E},{\mathbf B}$), and to…
For a group of charged particles obeying quantum mechanics interacting with an electromagnetic field, the charge and current density in a pure state of the system are expressed with the many-body wave function of the state. Using these as…
A three-polar, cf. T. Gregor, J. Halu\v{s}ka, Lexicographical ordering and field operations in the complex plane. Stud. Mat. 41(2014), 123--133., $HSV-RGB$ Colour space $\triangle$ was introduced and studied. It was equipped with operations…
A systematic description of multipole degrees of freedom is discussed on the basis of the Stevens' operator-equivalent technique. The generalized Stevens' multiplicative factors are derived for all of the electric and the magnetic…
While causal perturbation theory and lattice regularisation allow treatment of the ultraviolet divergences in qed, they do not resolve the issues of constructive field theory, or show the validity of qed except as a perturbation theory. I…
A robust and efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector Helmholtz…