Massless Elementary Particles in a Quantum Theory over a Galois Field

We consider massless elementary particles in a quantum theory based on a Galois field (GFQT). We previously showed that the theory has a new symmetry between particles and antiparticles, which has no analogue in the standard approach. We now prove that the symmetry is compatible with all operators describing massless particles. Consequently, massless elementary particles can have only half-integer spin (in conventional units), and the existence of massless neutral elementary particles is incompatible with the spin–statistics theorem. In particular, this implies that the photon and the graviton in the GFQT can only be composite particles.