2002•arXiv (Cornell University)Open access
Do Neutral Elementary Particles Exist
Felix M. Lev
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Abstract
We consider massless elementary particles in quantum theory based on a Galois field (GFQT). In our recent paper hep-th/0206078 where the GFQT has been discussed in detail, it has been shown that the theory possesses a new symmetry between particles and antiparticles, which has no analog in the standard approach. In the present paper we prove that the symmetry is compatible with all the operators describing massless particles. As a consequence, the existence of massless neutral elementary particles in the GFQT is incompatible with the usual relation between spin and statistics (in particular, this implies that in the GFQT, the photon and the graviton can be only composite particles). We argue that the same statement is also valid for neutral particles with arbitrary masses.