Nonuniqueness of gravity-induced fermion interaction in the Einstein-Cartan theory

TL;DR

This paper investigates the nonuniqueness in the minimal coupling procedure of Einstein-Cartan gravity with fermions, showing how different choices affect predictions and proposing solutions for making the theory experimentally testable.

Contribution

It demonstrates the impact of divergence additions to the fermionic Lagrangian on gravity-induced interactions and argues for resolving nonuniqueness to enable experimental verification of Einstein-Cartan theory.

Findings

Gravity-induced four-fermion interaction has unexpected features.

Proper choice of fermionic Lagrangian can make EC theory indistinguishable from General Relativity.

Addressing nonuniqueness is essential for experimental tests of EC-based theories.

Abstract

The problem of nonuniqueness of minimal coupling procedure for Einstein--Cartan (EC) gravity with matter is investigated. It is shown that the predictions of the theory of gravity with fermionic matter can radically change if the freedom of addition of a divergence to the flat space matter Lagrangean density is exploited. The well--known gravity induced four--fermion interaction is shown to reveal unexpected features. The solution to the problem of nonuniqueness of minimal coupling of EC gravity is argued to be necessary in order for the theory to produce definite predictions. In particular, the EC theory with fermions is shown to be indistinguishable from usual General Relativity on the effective level, if the flat space fermionic Lagrangean is appropriately chosen. Hence, the solution to the problem of nonuniqueness of minimal coupling procedure is argued to be necessary if EC theory is to be experimentally verifiable. It could also enable experimental tests of theories based on EC, such as loop approach to quantisation of gravitational field. Some ideas of how the arbitrariness incorporated in EC theory could be restricted or even eliminated are presented.