On the coupling of massless particles to scalar fields

TL;DR

This paper examines whether massless particles can interact with scalar fields within a special relativistic framework, concluding that such coupling does not alter their trajectories, unlike massive particles which are affected even at high speeds.

Contribution

It demonstrates that in a Lorentz-invariant classical theory, massless particles do not couple to scalar fields, contrasting with the influence observed on massive particles.

Findings

Massless particles follow straight-line trajectories unaffected by scalar fields.

Massive particles are influenced by scalar fields even in the ultra-relativistic limit.

Coupling of massless particles to scalar fields is trivial in the considered theory.

Abstract

It is investigated if massless particles can couple to scalar fields in a special relativistic theory with classical particles. The only possible obvious theory which is invariant under Lorentz transformations and reparametrization of the affine parameter leads to trivial trajectories (straight lines) for the massless case, and also the investigation of the massless limit of the massive theory shows that there is no influence of the scalar field on the limiting trajectories. On the other hand, in contrast to this result, it is shown that massive particles are influenced by the scalar field in this theory even in the ultra-relativistic limit.