On the Uniqueness of Einstein-Cartan Theory: Lagrangian, Covariant Derivative and Equation of Motion

TL;DR

This paper addresses ambiguities in Einstein-Cartan theory by proposing a new covariant derivative, clarifying how matter fields couple to gravity, and comparing this approach with previous methods.

Contribution

It introduces a novel covariant derivative to resolve coupling ambiguities in Einstein-Cartan theory and analyzes its relation to prior treatments.

Findings

Proposed a new covariant derivative eliminating coupling ambiguity

Clarified the relation between the new approach and previous treatments

Enhanced understanding of matter-gravity coupling in Einstein-Cartan theory

Abstract

In the standard Einstein-Cartan theory(EC), matter fields couple to gravitation field through the Minimal Coupling Procedure(MCP), yet leaving the theory an ambiguity: applying MCP to the action or to the equation of motion would lead to different gravitational couplings. We propose a new covariant derivative to remove the ambiguity, then discuss the relation between our proposal and previous treatments on this subject.