Related papers: The Dirac equation in general relativity, a guide …
A relationship between the discrete Dirac-K\"ahler equation and discrete analogues of some Dirac type equations in the geometric spacetime algebra is discussed. We show that a solution of the discrete Dirac-K\"ahler equation can be…
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitational fields can be incorporated as background spacetime if the…
Following our work from the previous paper about the study of effective Dirac algebra and the metric of the simple, special case of relativistic hydrogen atom, this paper gives the complete metric study defined by the effective Dirac…
The work is devoted to the generalization of the Dirac equation for a flat locally anisotropic, i.e., Finslerian space-time. At first we reproduce the corresponding metric and a group of the generalized Lorentz transformations, which has…
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
The goal of this work is to extend Dirac-type tensor equations to a curved space. We take four 1-forms (a tetrad) as a unique structure, which determines a geometry of space-time.
Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a…
We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation…
A peculiar representation of the Lorentz group is suggested as a starting point for a consistent approach to relativistic quantum theory.
Due to some current interest in this subject we have produced this note. There is no claim to anything new, except possibly to show that a direct numerical approach is quite simple and instructive. For comparison purposes we include a…
We present a general formulation for ray-tracing calculations in curved space-time. The formulation takes full account of relativistic effects in the photon transport and the relative motions of the emitters and the light-of-sight absorbing…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…
Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
It is shown that in the case of the spherically symmetric static backgrounds there is a gauge in which the Dirac equation is manifestly covariant under rotations. This allows us to separate the spherical variables like in the flat…
These Lecture notes give an introduction to Regge calculus as a discrete model of General Relativity.
We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. We aim to find general relativistic corrections to the quantum theory of particles affected by Newtonian gravity, a regime nowadays…
We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor…
The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries. Our method is inspired in the geometric viewpoint developed by Gotay,…