Geometric Interpretation of Electromagnetism in a Gravitational Theory with Space--Time Torsion

Abstract

A complete geometric unification of gravity and electromagnetism is proposed by considering two aspects of torsion: its relation to spin established in Einstein--Cartan theory and the possible interpretation of the torsion trace as the electromagnetic potential. Starting with a Lagrangian built of Dirac spinors, orthonormal tetrads, and a complex rather than a real linear connection we define an extended spinor derivative by which we obtain not only a very natural unification, but can also fully clarify the nontrivial underlying fibre bundle structure. Thereby a new type of contact interaction between spinors emerges, which differs from the usual one in Einstein--Cartan theory. The splitting of the linear connection into a metric and an electromagnetic part together with a characteristic length scale in the theory strongly suggest that gravity and electromagnetism have the same geometrical origin.