Symmetries in a unified gauge theory with torsion

TLDR: In this paper, a generalization of the Bonnor-moffat-Boal formulation of Einstein unified field theory is considered, where the curvature tensor is replaced with a generalized torsion containing connection.

Abstract: We consider aGL4×Un generalization of the Bonnor-Moffat-Boal formulation of Einstein unified field theory. Choosing a suitable form of the curvature tensor and introducing a phenomenological electric-current density, we show that charge conjugation corresponds to complex conjugation of the nonsymmetric unified fields. Making use of the complex tetrads underlying the fundamental Hermitian tensor field, we show that the gauge-covariant Dirac equation is obtained by minimal replacement of the Christoffel affinity of GR, with the generalized torsion containing connection. Finally, we consider spontaneous breaking of theUn gauge symmetry. The formalism splits into a vector sector and a tensor sector, the rotation angles\(\theta _W \) and\(\theta _G \) diagonalizing the vector and tensor mass matrices being related by\(\theta _G = \theta _W + \frac{1}{2}\pi \). TheUn components of the torsion vector describe the vector bosons mediating the electromagnetic and weak interactions, while theUn components of the symmetric part of the fundamental tensor describe the graviton and aSUn multiplet of tensor mesons.