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

Understand

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.