A note on Dirac spinors in a non-flat space-time of general relativity

Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromagnetic field, and to one subjected to geodesic motion in a static metric, and leads to the same, usual form of the Dirac equation--in special coordinates. To use the equation in the...

This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the Dirac equation, operators and monogenics, the Hydrogen atom, propagators and scattering theory, spin precession, tunnelling times, spin measurement, multiparticle quantum mechanics, relativistic multiparticle wave equations, and semiclassical ...

It is proven that the usual quadratic general-covariant Lagrangian for the Dirac field leads to a symmetric, divergence-free energy-momentum tensor in the standard Riemannian framework of space-time without torsion, provided the tetrad field components are the only quantities related to gravitation that are varied independently.

A unified approach to the study of classical and quantum spin in external fields is developed. Understanding the dynamics of particles with spin and dipole moments in arbitrary gravitational, inertial and electromagnetic fields is important in astrophysics and high-energy and heavy-ion experimental physics.

We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.

The inertial and gravitational properties of intrinsic spin are discussed and some of the recent work in this area is briefly reviewed. The extension of relativistic wave equations to accelerated systems and gravitational fields is critically examined. A nonlocal theory of accelerated observers is presented and its predictions are compared with observation.

The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy-Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime metric is realized. In this representation the Hamiltonian provides for a coupling between spin and gravity through the torsion of the gravitational field. In the specific case of a symmetric gravitational field we retrieve the Hamiltonian ...

In this article, various approaches to calculate covariant expressions for the bilinears of Dirac spinors are presented. For this purpose, algebraic equations defining Dirac spinors are discussed. Following that, a covariant approach for spacetime parameterization is presented and the equations defining Dirac spinors are written fully in terms of Lorentz scalars. After presenting how the tensorial bilinears can be reduced to combinations of scalar bilinears with appropriate L...

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 for deriving the Dirac equation in Curved Spacetime make no mention of employing Einstein's field equation. Thus, to date, the literature on the derivation of the Dirac equation could not include an expression for the presence of matter. T...

In this paper, we study the non commutative quantum dynamics of the spinorial field in the presence of a gravitational background within DeWitt's approach. By employing the vierbein formalism in the temporal state of non commutative four-dimensional space time, we also analyze the first level correction of the solution and Green's function in terms of the Riemann curvature tensor. The effect of the gravitational background is imposed at least up to the first order of the Riem...