  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 the 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.
