Related papers: Relativistic Electrodynamics without Reference Fra…
Multivector quantum mechanics utilizes wavefunctions which are Clifford aggregates (e.g. sum of scalar, vector, bivector). This is equivalent to multi- spinors constructed of Dirac matrices, with the representation independent form of 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…
This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron…
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these…
Aristotelian electrodynamics (AE) describes the regime of a plasma with a very strong electric field that is not shorted out, with charge current determined completely by pair production and the balance of Lorentz 4-force against curvature…
Closed form expressions in a coordinate-free form in real Clifford geometric algebras (GAs) Cl(0,3), Cl(3,0)$, Cl(1,2) and Cl(2,1) are found for exponential function when the exponent is the most general multivector (MV). The main…
In this work, a non-relativistic theory of the electroscalar field being an expansion of the classical Maxwell's electrodynamics is presented. Expansion of the classical electrodynamics is based on the hypothesis about an existing new…
In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford…
In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B respectively, are examined using…
In this paper we show how all the quantum properties of Schroedinger and Pauli particles can be described entirely from within a Clifford algebra taken over the reals. There is no need to appeal to any `wave function'. To describe a quantum…
Force-free electrodynamics is the theoretical paradigm used to describe electromagnetic fields in a region where the inertia of plasma is negligible compared to the strength of the electromagnetic field. While these fields are studied…
We illustrate how our recent light-front approach simplifies relativistic electrodynamics with an electromagnetic (EM) field $F^{\mu\nu}$ that is the sum of a (even very intense) plane travelling wave $F_t^{\mu\nu}(ct\!-\!z)$ and a static…
We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the…
In the study of the electronic structure of heavy atoms, relativistic effects cannot be neglected and the Dirac operator naturally appears in place of the Schr\"odinger operator, raising a number of additional difficulties. The complexity…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's…
In this lecture we discuss some interesting developments in the modern theory of electromagnetic field(s). In particular, by using the methods developed in Dirac's constraint dynamics we derive the Schr\"{o}dinger equation for the free…
We study physical aspects for a new nonlinear electrodynamics (inverse electrodynamics). It is shown that this new electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field, hence we compute the…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…
We formulate a covariant version of Maxwell-like fracton electrodynamics in six dimensions using a symmetric tensor gauge field with scalar gauge symmetry $\delta A_{\mu\nu}=\partial_\mu\partial_\nu\Lambda$. This provides a relativistic…