General Dynamics of Spinors

TL;DR

This paper develops a Lorentz covariant framework for Dirac spinors in curved spacetime, revealing that spinors can be described by two real scalar fields, the module and Yvon-Takabayashi angle, and explores their coupling to curvature and torsion.

Contribution

It introduces a real, Lorentz covariant decomposition of Dirac spinors in curved spacetime, simplifying the field equations and highlighting the roles of the module and Yvon-Takabayashi angle.

Findings

Spinors can be described by two real scalar fields.

The field equations are real and Lorentz covariant.

Coupling of curvature and torsion to the scalar fields is analyzed.

Abstract

In this paper, we consider a general twisted-curved space-time hosting Dirac spinors and we take into account the Lorentz covariant polar decomposition of the Dirac spinor field: the corresponding decomposition of the Dirac spinor field equation leads to a set of field equations that are real and where spinorial components have disappeared while still maintaining Lorentz covariance. We will see that the Dirac spinor will contain two real scalar degrees of freedom, the module and the so-called Yvon-Takabayashi angle, and we will display their field equations. This will permit us to study the coupling of curvature and torsion respectively to the module and the YT angle.