Modified coupling procedure for the Poincar\'e gauge theory of gravity

TL;DR

This paper proposes a slight modification to the minimal coupling procedure in Poincaré gauge theory of gravity, resolving ambiguities and ensuring unique predictions, especially in Einstein-Cartan theory with fermions.

Contribution

It introduces a modified coupling procedure that clarifies and unifies the application of gauge principles in gravity theories, removing previous ambiguities.

Findings

Removes ambiguity in minimal coupling for gravity

Ensures unique predictions in Einstein-Cartan theory

Justifies earlier results in Poincaré gauge gravity

Abstract

The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincar\'e gauge theory of gravity. In particular, the predictions of the Einstein-Cartan theory with fermionic matter are rendered unique.