On the problem of Unicity in Einstein-Sciama-Kibble Theory

TL;DR

This paper examines the Einstein-Sciama-Kibble (ESK) theory, demonstrating how the antisymmetry of spin and torsion restricts the form of matter fields, favoring the simplest case over more general theories.

Contribution

It shows that the complete antisymmetry of spin in ESK theory constrains matter field theories to a unique simple form, excluding more complex possibilities.

Findings

Complete antisymmetry of spin constrains matter fields

Only the simplest matter field theory is compatible with antisymmetric torsion

More general matter theories are excluded by antisymmetry constraints

Abstract

We consider the ESK theory, based on the principle for which the space is filled with matter fields in such a way that Cartan torsion is spin; in the geometry in which Cartan torsion tensor is completely antisymmetric, spin has to be completely antisymmetric: we will show how the complete antisymmetry of spin constraints the form of possible matter field theories as to allow the special case of the simplest one solely, all other most general cases being excluded.