Related papers: Nonlinear Electromagnetic Self-Duality and Legendr…
Hamilton equations based not only upon the Poincare--Cartan equivalent of a first-order Lagrangian, but rather upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton--De Donder theory, but…
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action…
Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions $f(\phi)$ and $g(\phi)$, depending on a real…
We study the interaction between dark matter and dark energy, with dark energy described by a scalar field having a double exponential effective potential. We discover conditions under which such a scalar field driven solution is a late…
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the…
Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the…
We investigate the electromagnetic dynamics of spin-nondegenerate classical particle models arising from Lorentz-violating sectors of the Standard-Model Extension, focusing on the $b_\mu$ background. Starting from the type-2 relativistic…
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…
The quantum mechanical transition between a free particle Lagrangian and the Klein Gordon field description of a free particle (particle wave duality) is conjectured to extend to an analogous construction of relativistically invariant wave…
Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre…
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…
The present work proposes a discussion on the self-energy of charged particles in the framework of nonlinear electrodynamics. We seek magnet- ically stable solutions generated by purely electric charges whose electric and magnetic fields…
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain…
In d=4 de Sitter space, novel conformally invariant photon-like theories consistently couple to charged matter. We show that these higher spin, maximal depth, partially massless systems enjoy a Maxwellian, "electric-magnetic" duality.
Electromagnetic duality is a symmetry of the source-free Einstein-Maxwell equations that rotates electric and magnetic fields while leaving the stress-energy tensor invariant. We present the first fully nonlinear realization of this…
Gauge transformations are potential transformations that leave only specific Maxwell fields invariant. To reveal more, I develop Lorenz field equations with full Maxwell form for nongauge, sans gauge function, transformations yielding…