Related papers: Born-Infeld electrodynamics: Clifford number and s…
An analogy with real Clifford algebras on even-dimensional vector spaces suggests to assign a couple of space and time dimensions modulo 8 to any algebra (represented over a complex Hilbert space) containing two self-adjoint involutions and…
The new derivation of the equation of the spin precession is given for a particle possessing electric and magnetic dipole moments. Contributions from classical electrodynamics and from the Thomas effect are explicitly separated. A fully…
The new spinor-unit field representation of the electromagnetism \cite{Nash2010} (with quark and lepton sources) is integrated via minimal coupling with standard Einstein gravitation, to formulate a Lagrangian model of the very early…
In these notes we introduce the Clifford algebra of a quadratic space using techniques from universal algebra and algebraic theory of quadratic forms. We also define the Clifford, Pin and Spin groups associated to the algebra, and study how…
Prompted by a recent demonstration that the structure of a single quark-lepton generation may be understood via a Dirac-like linearization of the form p^2+x^2, we analyze the corresponding Clifford algebra in some detail. After classifying…
One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…
The structure of 29-dimensional extended real Clifford-Dirac algebra, which has been introduced in our paper Phys. Lett. A, 2011, 375, 2479, is considered in brief. Using this algebra, the property of Fermi-Bose duality of the Dirac…
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…
We formulate a nonlinear electrodynamic theory which may be viewed as a weighted theory minimally interpolating the classical Maxwell and Born--Infeld theories. We show that, in contrast to the Born--Infeld theory, this new theory…
We obtain the characteristic equation for the nonlinear Born-Infeld electrodynamics. This equation has the form of the characteristic equation for the linear electrodynamics in some effective Riemann space. The effective metric include the…
We consider the Born-Infeld nonlinear electromagnetic field equations and study its Cauchy problem in the case that the Vlasov equation is considered as a matter model. In the present paper, the Vlasov equation is considered on the…
In this paper we present the formulation of relativistic electrodynamics (independent of the reference frame and of the chosen system of coordinates in it) that uses the Faraday bivector field F. This formulation with F field is a…
A new concept for the geometrisation of electromagnetic interaction is proposed. Instead of the concept "extended field--point sources", interacting Maxwell's and Dirac's fields are considered as a unified closed noneuclidean and…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
In the field theories with twistor structure particles can be identified with (spacially bounded) caustics of null geodesic congruences defined by the twistor field. As a realization, we consider the ``algebrodynamical'' approach based on…
All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld…
Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces to construct a certain positive-dimensional family of irreducible…
We present the first nonperturbative numerical calculations of the nonrelativistic hydrogen spectrum as predicted by first-quantized electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also show rigorous upper and lower…
We further explore the idea that physics takes place in Clifford space which should be considered as a generalization of spacetime. Following the old observation that spinors can be represented as members of left ideals of Clifford algebra,…
We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently, the holonomy algebras of certain spin connections in flat space. We provide series of examples in arbitrary dimensions and establish…