We reexamine the minimal coupling procedure in Hestenes' geometric algebra formulation of Dirac equation, where spinors are identified with even elements real Clifford spacetime. This point view, as we argue, leads naturally to a non-Abelian generalisation electromagnetic gauge potential.

D.M. Gitman, A.D. Levin, I.V. Tyutin, and B.L. Voronov Institute of Physics, University of Sao Paulo, Brazil Lebedev Physical Institute, Moscow, Russia The electronic struture of an atom with Z ≤ Zc = 137 can be described by the Dirac equation with the Coulomb field of a point charge Ze. It was believed that the Dirac equation with Z > Zc is inconsistent and physically meaningless because the f...

Herein, the Dirac equation is compared with the KleinGordon equation. In contrast to the Dirac case, it is proved that the Klein-Gordon equation has difficulties with the Hamiltonian differential operator of relativistic quantum mechanics and with the definition of an inner product of wave functions, which is a requirement for a construction of a Hilbert space. An added discussion of the Pauli-...

We formulate the boundary conditions near the atomic nucleus for solving the Pauli equation, based on the analytic solution of the Dirac equation for a Coulomb potential. We then integrate the Pauli equation using an effective potential that is adjusted to reproduce Dirac R-matrix scattering phase shifts, and find the (3)P(o)(1) resonance contribution to the photodetachment cross section of Cs-...

The aim of the present paper is to clarify the relationship between immersions of surfaces and solutions of the Dirac equation. The main idea leading to the description of a surface M 2 by a spinor eld is the observation that the restriction to M 2 of any parallel spinor on R 3 is a non-trivial spinor eld on M 2 of constant length which is a solution of the inhomogeneous Dirac equation. Vice ve...

1550-7998=20 The Lorentz-Dirac equation is not an unavoidable consequence of solely linear and angular momenta conservation for a point charge. It also requires an additional assumption concerning the elementary character of the charge. We here use a less restrictive elementarity assumption for a spinless charge and derive a system of conservation equations that are not properly the equation of...

In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigate what is now known as the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F = ψγ21˜ψ, wh...