Introduction to a Quantum Theory over a Galois Field
arXiv:1011.1076 · doi:10.3390/sym2041810
Abstract
We consider 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 (IR) of the symmetry algebra splits into independent IRs describing a particle an its antiparticle only in the approximation when de Sitter energies are much less than the characteristic of the field. As a consequence, the very notions of particles and antiparticles are only approximate and such additive quantum numbers as the electric, baryon and lepton charges are conserved only in this approximation. There can be no neutral elementary particles and the spin-statistics theorem can be treated simply as a requirement that standard quantum theory should be based on complex numbers.
43 pages, Latex, 1 figure
References in corpus (11)
- Measurements of Omega and Lambda from 42 High-Redshift Supernovae
- Quantum Gravity In De Sitter Space
- p-Adic Mathematical Physics
- A measurement of Omega from the North American test flight of BOOMERANG
- What is Quantum Field Theory, and What Did We Think It Is?
- Living with Infinities
- Fermions in (Anti) de Sitter Gravity in Four Dimensions
- Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions
- Huyghens, Bohr, Riemann and Galois: Phase-Locking
- Supersymmetry in Quantum Theory Over a Galois Field
- Quantum Theory on a Galois Field