Inconsistency of point-particle dynamics on higher-spin backgrounds: massive particles

TL;DR

This paper demonstrates that both massless and massive point particles cannot propagate consistently on chiral higher-spin backgrounds due to inherent non-locality in the Hamiltonians, extending previous massless results.

Contribution

It extends prior work by showing massive particles also cannot propagate on chiral higher-spin backgrounds, using a direct approach that reveals non-local Hamiltonians.

Findings

Massive particles cannot propagate on chiral higher-spin backgrounds.

All consistent Hamiltonians are necessarily non-local.

The approach connects light-cone consistency with on-shell worldline methods.

Abstract

Previously, we showed that massless scalar point particles cannot propagate on classical backgrounds of chiral higher-spin theory. This conclusion was derived from the analysis of the light-cone consistency conditions occurring at the second order in interactions. In the present paper, we extend this result to the case of massive particles, showing that these cannot propagate on chiral higher-spin backgrounds either. In order to do that, we use a different and more direct approach, which does not rely on special simplifications occurring for massless particles. Namely, we solve the light-cone consistency conditions at the given order in complete generality and then show that all the Hamiltonians found are inevitably non-local. We emphasise connections between the resulting procedure and the on-shell methods applied to worldline scattering observables.