Related papers: Introducing Multidimensional Dirac-Hestenes Equati…

This paper investigates the Lorentz invariance of the multidimensional Dirac-Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the coordinates. We examine two distinct…

We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which…

Attention is given to the interface of mathematics and physics, specifically noting that fundamental principles limit the usefulness of otherwise perfectly good mathematical general integral solutions. A new set of multivector solutions to…

We derive a Dirac-like equation, the asymmetric Dirac equation, where particles and antiparticles sharing the same wave number have different energies and momenta. We show that this equation is Lorentz covariant under proper Lorentz…

In this paper using the apparatus of the Clifford bundle formalism we show how straightforwardly solve in Minkowski spacetime the Dirac-Hestenes equation -- which is an appropriate representative in the Clifford bundle of differential forms…

Discrete models of the Dirac-K\"{a}hler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.

We discuss the variational principle within Quantum Mechanics in terms of the noncommutative even Space Time sub-Algebra, the Clifford $\Ra$-algebra $Cl_{1,3}^+$. A fundamental ingredient, in our multivectorial algebraic formulation, is the…

We reexamine the minimal coupling procedure in the Hestenes' geometric algebra formulation of the Dirac equation, where spinors are identified with the even elements of the real Clifford algebra of spacetime. This point of view, as we…

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…

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…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…

We present a high-precision solution of Dirac equation by numerically solving the minmax two-center Dirac equation with the finite element method (FEM). The minmax FEM provide a highly accurate benchmark result for systems with light or…

We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…

It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…

The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…

Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…

In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…

In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…

Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering…

We discuss the structure of the Dirac equation and how the nilpotent and the Majorana operators arise naturally in this context. This provides a link between Kauffman's work on discrete physics, iterants and Majorana Fermions and the work…