Consistency Conditions on the S-Matrix of Massless Particles

TL;DR

This paper establishes strict consistency conditions for the S-matrix of massless particles in four-dimensional space, showing that most such theories must have trivial S-matrices unless specific criteria are met.

Contribution

It introduces a new set of consistency conditions for constructible theories of massless particles, providing a systematic approach to identify non-trivial S-matrix theories.

Findings

Proves the impossibility of non-trivial S-matrices for spins greater than 2.

Shows the non-existence of interacting multiple spin 2 particles.

Demonstrates the uniqueness of theories with spin 2 and spin 3/2 particles.

Abstract

We introduce a set of consistency conditions on the S-matrix of theories of massless particles of arbitrary spin in four-dimensional Minkowski space-time. We find that in most cases the constraints, derived from the conditions, can only be satisfied if the S-matrix is trivial. Our conditions apply to theories where four-particle scattering amplitudes can be obtained from three-particle ones via a recent technique called BCFW construction. We call theories in this class constructible. We propose a program for performing a systematic search of constructible theories that can have non-trivial S-matrices. As illustrations, we provide simple proofs of already known facts like the impossibility of spin $s > 2$ non-trivial S-matrices, the impossibility of several spin 2 interacting particles and the uniqueness of a theory with spin 2 and spin 3/2 particles.