Elementary Particles in a Quantum Theory Over a Galois Field
Abstract
Description
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 spin-statistics 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.
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
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