Elementary Particles in a Quantum Theory Over a Galois Field
Abstract
We consider elementary particles in a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily describes a particle and its antiparticle simultaneously. {\it In other words, the very existence of antiparticles is a strong indication that nature is described rather by a finite field (or at least a field with a nonzero characteristic) than by complex numbers.} As a consequence, the spinstatistics theorem is simply a requirement that standard quantum theory should be based on complex numbers and elementary particles cannot be neutral. The Dirac vacuum energy problem has a natural solution and the vacuum energy (which in the standard theory is infinite and negative) equals zero as it should be.
 Publication:

arXiv eprints
 Pub Date:
 August 2002
 arXiv:
 arXiv:hepth/0209001
 Bibcode:
 2002hep.th....9001L
 Keywords:

 High Energy Physics  Theory
 EPrint:
 Latex, 37 pages, no figures. Minor changes in motivation. In particular, it is noted that the very existence of antiparticles is a strong indication that nature is described rather by a finite field (or at least a field with a nonzero characteristic) than by complex numbers