Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"

TL;DR

This paper demonstrates that Dirac spinor fields can be consistently coupled with the gravitational field in teleparallel gravity, resolving previous issues by proposing an alternative coupling approach.

Contribution

It clarifies the coupling of spinor fields in teleparallel gravity and shows that previous consistency problems are specific to a particular coupling choice.

Findings

Consistency achieved with an alternative coupling method

Problems are specific to a particular coupling choice

Supports the viability of Dirac fields in teleparallel gravity

Abstract

We show that the coupling of a Dirac spinor field with the gravitational field in the teleparallel equivalent of general relativity is consistent. For an arbitrary SO(3,1) connection there are two possibilities for the coupling of the spinor field with the gravitational field. The problems of consistency raised by Y. N. Obukhov and J. G. Pereira in the paper {\it Metric-affine approach to teleparallel gravity} [gr-qc/0212080] take place only in the framework of one particular coupling. By adopting an alternative coupling the consistency problem disappears.