Implications of nonsymmetric metric theories for particle physics: New interpretation of the Pauli coupling

Abstract

In this work, we provide a possible geometrical interpretation of the spin of elementary particles. In particular, it is investigated how the wave equations of matter are altered by the addition of an antisymmetric contribution to the metric tensor. In this scenario, the explicit form of the matter wave equations is investigated in a general curved spacetime, and then the equations are particularized to the flat case. Unlike traditional approaches of Nonsymmetric Gravitational Theories (NGT), in which the gravitational field is responsible for breaking the symmetry of the flat Minkowski metric, we find more natural to consider that, in general, the metric of the spacetime could be nonsymmetric even in the flat case. The physical consequences of this assumption are explored in detail. Interestingly enough, it is found that the metric tensor splits into a bosonic and a fermionic; the antisymmetric part of the metric is very sensitive to the spin and turns out to be undetectable for spinless scalar particles. However, fermions couple to it in a nontrivial way (only when there are interactions). In addition, the Pauli coupling is derived automatically as a consequence of the nonsymmetric nature of the metric.