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

TL;DR

This paper explores a geometric interpretation of particle spin through nonsymmetric metric theories, revealing how such metrics influence matter wave equations and naturally derive the Pauli coupling, especially affecting fermions.

Contribution

It introduces a novel perspective where nonsymmetric metrics in flat spacetime influence particle spin and derive the Pauli coupling without traditional assumptions.

Findings

Nonsymmetric metrics can exist in flat spacetime and influence particle properties.

Fermions couple to the antisymmetric part of the metric in a non-trivial way.

The Pauli coupling emerges naturally from the nonsymmetric metric framework.

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 space-time, and then the equations are particularized to the flat case. Unlike traditional approaches of 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 space-time 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 non-trivial way (only when there are interactions). In addition, the Pauli coupling is derived automatically as a consequence of the nonsymmetric nature of the metric