Lessons of spin and torsion: Reply to ``Consistent coupling to Dirac fields in teleparallelism"

TL;DR

This paper defends the position that coupling Dirac fields to teleparallel gravity is fundamentally inconsistent, a problem that extends to all spinning sources, challenging certain generalizations in teleparallel theories.

Contribution

The paper explicitly demonstrates the inherent inconsistency in coupling Dirac and other spinning fields to teleparallel gravity, countering recent criticisms.

Findings

Coupling of Dirac fields to teleparallel gravity is inconsistent.

The inconsistency applies broadly to all sources with spin.

Generalizations of spinor fields do not resolve the issue.

Abstract

In reply to the criticism made by Mielke in the pereceding Comment [Phys. Rev. D69 (2004) 128501] on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for {\it all} sources with spin and is by no means restricted to the Dirac field. In this sense the $SL(4,R)$-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.