Is the Mass Scale for Elementary Particles Classically Determined?

TL;DR

This paper explores whether elementary particle masses can be derived from classical interactions with distant matter in a universe with negative curvature, within the framework of conformal gravity, suggesting a possible mechanism for mass generation.

Contribution

It proposes a classical mechanism involving distant matter and vector potentials in curved space to explain the origin of particle mass, linked to symmetry breaking.

Findings

Distant matter influences the vector potential squared, A^2.

Non-thermal contributions to A^2 dominate over thermal parts.

A Coleman-Weinberg type symmetry breaking transition can generate particle masses.

Abstract

We investigate whether a mass scale for elementary particles can be derived from interactions of particles with distant matter in the Universe, the mechanism of the interaction being the classical vector potential, propagating in a space of negative curvature. A possible context for such a mass scale is conformal gravity. This theory may prove to be renormalizable, since all coupling constants are dimensionless; conversely, however, there is no coupling constant analogous to the conventional G to provide a starting point for a mass scale calculation. We obtain the equations for propagation of the vector potential of a charged particle moving in a plasma in a curved space. We then show that distant matter will contribute to A**2, and that this non-thermal part will eventually dominate the ordinary thermal part. At this point a symmetry breaking transition of the Coleman-Weinberg type is possible, and particle masses can be generated with m**2 of order A**2.