No-interaction theorem without Hamiltonian and Lagrangian formalism: invariant momentum on null cones

TL;DR

This paper extends the no-interaction theorem by proving that four particles cannot interact if their invariant momentum on null cones remains constant, without relying on Hamiltonian or Lagrangian formalism.

Contribution

It introduces a new invariance assumption on null cones and demonstrates the no-interaction result under this condition, broadening the theorem's applicability.

Findings

No interaction for four particles with invariant null cone momentum

Null cone invariance leads to no-interaction conclusion

Generalizes previous space-like plane results

Abstract

In a previous paper (G.Yoneda, Proc.R.Soc.London, A445,(1994),221), we proved the no-interaction theorem for four particles with the assumption that the (linear and angular) momentum on space-like planes is invariant. In this paper, we assume that the momentum on null cones is invariant and prove that there is no interaction for four particles.