Related papers: Quaternionic Electron Theory: Dirac's Equation
This work analyzes monolayer graphene in external electromagnetic fields, which is described by the Dirac equation with minimal coupling. Supersymmetric quantum mechanics allows building new Dirac equations with modified magnetic fields.…
We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…
Quaternions were appeared through Lagrangian formulation of mechanics in Symplectic vector space. Its general form was obtained from the Clifford algebra, and Frobenius' theorem, which says that "the only finite-dimensional real division…
We prove that the classical Dirac equation in the presence of an external (nondynamical) electromagnetic field is a relativistically causal theory. As a corollary, we show that it is impossible to use quantum tunneling to transmit particles…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
The present paper is the continuity of the previous papers "Non-linear field theory" I and II. Here on the basis of the electromagnetic representation of Dirac's electron theory we consider the geometrical distribution of the…
Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, achieved by multiplying one of the gamma matrices by the imaginary number, $i$. The reason for doing this is to…
We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…
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…
The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of…
A representation of the Dirac algebra, derived from first principles, can be related to the combinations of unit charges which determine particle structures. The algebraic structure derives from a broken symmetry between 4-vectors and…
We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For…
In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
We point out that in a recent paper by Chaichian et al. (Phys. Rev.Lett71(1993)3405) Dirac quantization procedure is not properly followed as a result of which the resulting quantum theory is different from what one will get by a…
It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…