Massless Elementary Particles in a Quantum Theory over a Galois Field

@article{Lev2002MasslessEP,
  title={Massless Elementary Particles in a Quantum Theory over a Galois Field},
  author={Felix M. Lev},
  journal={Theoretical and Mathematical Physics},
  year={2002},
  volume={138},
  pages={208-225}
}
  • F. Lev
  • Published 22 July 2002
  • Physics
  • Theoretical and Mathematical Physics
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 half-integer spin (in conventional units), and the existence of massless neutral elementary particles is… 

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References

SHOWING 1-10 OF 58 REFERENCES

Problem of constructing discrete and finite quantum theory

We consider in detail an approach (proposed by the author earlier) where quantum states are described by elements of a linear space over a Galois field, and operators of physical quantities - by

Finiteness of physics and its possible consequences

  • F. Lev
  • Mathematics, Physics
  • 1993
The modular analog of representations of the so(1,4) algebra for a system of two spinless particles is considered in the framework of approach (proposed by the author earlier), in which physical

Quantum Theory of Fields

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject. But it is a very good and most useful book. The original was

Elementary particles in a curved space

The Fierz-Pauli program is carried out for spin-2 fields in-de Sitter space. A spin-s field is associated with an irreducible representation D(E0, s) of the universal covering group of SO(3, 2), with

One massless particle equals two Dirac singletons

The ‘remarkable representations of the 3+2 de Sitter group’, discovered by Dirac, later called singleton representations and here denoted Di and Rac, are shown to possess the following truly

SO(3,2)-invariant scattering and dirac singletons

We construct representations of a fourfold covering group of SO/sub 0/(3,2) (metaplectic group) by para-Bose operators. An SO/sub 0/(3,2)-invariant scattering theory is presented, showing especially

The Connection Between Spin and Statistics

In the following paper we conclude for the relativistically invariant wave equation for free particles: From postulate (I), according to which the energy must be positive, the necessity of

Modular representations as a possible basis of finite physics

The approach in which physical systems are described by the elements of a linear space over a finite field, and operators of physical quantities by linear operators in this space, is discussed. The

Restricted representations of classical Lie algebras of types $A_2$ and $B_2$

The dimensions of the finite dimensional irreducible restricted modules for a Lie algebra of classical type have never been determined. C. W. Curtis ([5], [6]) has given sufficient, but not

Representations of the Galilei group

SummaryWhile the transition to a moving coordinate system (x→x+vt, t→t) commutes in classical mechanics with displacements (x→x+a, t→t), the corresponding operations in Schrödinger's nonrelativistic
...