Worldline account of the no‑go theorem for massless charged particles

Determine, within the first‑quantized worldline BRST formulation of the bosonic spinning particle coupled to an abelian electromagnetic background, how the no‑go theorem forbidding massless charged particles (Weinberg–Witten type) manifests itself. In particular, establish a worldline derivation or explanation of the obstruction to a consistent (nilpotent) BRST charge in the massless charged case beyond the spin‑1 sector, clarifying the precise mechanism and conditions under which the theorem emerges in this framework.

Background

In Section 2.2.2, the thesis analyzes the BRST quantization of a bosonic spinning particle interacting with an abelian electromagnetic background. The construction shows that for spin s=0 the BRST charge is nilpotent off shell, and for spin s=1 it becomes nilpotent provided the background solves Maxwell’s equations. For higher spins the algebra generally fails to be first‑class and nilpotency is obstructed.

The authors connect this observation to the classic no‑go result on massless charged particles (Weinberg–Witten), noting that while the worldline analysis captures some of the obstructions, a direct worldline derivation of the no‑go theorem is not yet available. Understanding this correspondence would clarify the limits of consistent couplings in the worldline approach and sharpen the relation between BRST nilpotency and no‑go constraints.