Weak gauge principle and electric charge quantization

TL;DR

This paper revises the argument for electric charge quantization using a weak gauge principle, especially in spacetimes with torsion, proposing new topological origins for charge units and implications for quark color charge.

Contribution

It introduces a new approach to charge quantization considering spacetimes with torsion, and suggests topological origins for electric and color charges, extending previous theories.

Findings

Charge quantization depends on non-exact electromagnetic fields.

Spacetimes with torsion allow topologically non-trivial charged configurations.

Color charge may have a topological origin related to torsion subgroup order.

Abstract

Starting from a weak gauge principle we give a new and critical revision of the argument leading to charge quantization on arbitrary spacetimes. The main differences of our approach with respect to previous works appear on spacetimes with non trivial torsion elements on its second integral cohomology group. We show that in these spacetimes there can be topologically non-trivial configurations of charged fields which do not imply charge quantization. However, the existence of a non-exact electromagnetic field always implies the quantization of charges. Another consequence of the theory for spacetimes with torsion is the fact that it gives rise to two natural quantization units that could be identified with the electric quantization unit (realized inside the quarks) and with the electron charge. In this framework the color charge can have a topological origin, with the number of colors being related to the order of the torsion subgroup. Finally, we discuss the possibility that the quantization of charge may be due to a weak non-exact component of the electromagnetic field extended over cosmological scales.