Related papers: Matrix Representation of Special Relativity
Nonrelativstic effective field theories have shown to be a useful framework to describe systems of weakly bound particles. This work focuses on the matching procedure to the underlying relativistic theory. The concept of a physical mass in…
A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction,…
Matrix models of Yang-Mills type induce an effective gravity theory on 4-dimensional branes, which are considered as models for dynamical space-time. We review recent progress in the understanding of this emergent gravity. The metric is not…
We propose a gravitational theory in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor…
This work completes a serie of two papers devoted to the extension of the fundamental laws of electrodynamics in the context of Fock's nonlinear relativity (FNLR). Indeed, after having established in the previous study the exact…
The special theory of relativity has fundamentally changed our views of space and time. The relativity of simultaneity in particular, and the theory of relativity as a whole, still presents significant difficulty for beginners in the…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model…
We present a generalized velocity gauge form of the relativistic laser-matter interaction. In comparison with the (equivalent) regular minimal coupling description, this new form of the light-matter interaction results in superior…
The canonical formulation of general relativity is based on decomposition space--time manifold $M$ into $ R\times \Sigma$, this decomposition has to preserve the invariance of general relativity, invariance under general coordinates, and…
Assume that in a Lorentzian frame is given a relativistically admissible trajectory of a point mass. An event in such a frame can be described by four coordinates, first three representing the position and the last one the time of the…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
Many Lagrangians of physical theories can be expressed as eigenvalues of certain, relatively simple, matrices involving Dirac gamma matrices. We give concrete examples for Lagrangian corresponding to a point particle coupled to…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
In this work, we present two alternative yet equivalent representation formulae for Whitney forms that are valid for any choice of coordinates, and generalizes the original characterization of Whitney forms in Whitney (1957) that requires…
In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous Lorentz group. We also sketch those parts of…
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…