Related papers: Lanczos's functional theory of electrodynamics: A …
A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…
Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that…
The classical Blasius--Chaplygin formula provides an elegant method for calculating the lift force on a two-dimensional body in steady, irrotational flow. The key ingredient is the definition of a complex-valued potential function…
We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B-field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
We present a new formulation of self-dual nonlinear electrodynamics in which interactions are determined by an auxiliary-field potential, with causality ensuring a unique solution to the auxiliary-field equation. The long-standing problem…
In this paper we show how relativistic tensor dynamics and relativistic electrodynamics can be formulated in a biquaternion tensor language. The treatment is restricted to mathematical physics, known facts as the Lorentz Force Law and the…
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the…
Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
Starting with the quaternionic Minkowski space-time and its four-vector representation, a rotational analogue of the quaternionic Dirac equation in the electromagnetic field is developed, which includes not only the energy solutions but…
Around mid-1970s W. M. Tulczyjew discovered an approach which brings the two formalisms under a common geometric roof: the dynamics of a particle with configuration space $X$ is determined by a Lagrangian submanifold $D$ of $TT^*X$ (the…
We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical…
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency…
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the…
We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in $1/c$. Using a Lagrangian approach, we obtain the self-consistent charge and…
An effective model for describing the relativistic quantum dynamics of a radiating electron is developed via a relativistic generalization of the Lindblad master equation. By incorporating both radiation reaction and vacuum fluctuations…
The Liouville-Lanczos approach to linear-response time-dependent density-functional theory is generalized so as to encompass electron energy-loss and inelastic X-ray scattering spectroscopies in periodic solids. The computation of virtual…
Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for…