Massless Elementary Particles in a Quantum Theory over a Galois Field

  title={Massless Elementary Particles in a Quantum Theory over a Galois Field},
  author={Felix M. Lev},
  journal={Theoretical and Mathematical Physics},
  • 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… 

Quantum Theory over a Galois Field and Applications to Gravity and Particle Theory

We argue that the main reason of crisis in quantum physics is that nature, which is fundamentally discrete, is described by continuous mathematics. Moreover, no ultimate physical theory can be based

Dirac Singletons in a Quantum Theory over a Galois Field

Dirac singletons are exceptional irreducible representations (IRs) of the so(2,3) algebra found by Dirac. As shown in a seminal work by Flato and Fronsdal, the tensor product of singletons can be

Existence of Antiparticles as an Indication of Finiteness of Nature

  • F. Lev
  • Mathematics, Physics
  • 2010
It is shown that in a quantum theory over a Galois field, the famous Dirac's result about antiparticles is generalized such that a particle and its antiparticle are already combined at the level of

Symmetries in Foundation of Quantum Theory and Mathematics

  • F. Lev
  • Physics, Mathematics
  • 2020
FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

de Sitter symmetry and neutrino oscillations

Although the phenomenon of neutrino oscillations is confirmed in many experiments, the theoretical explanation of this phenomenon in the literature is essentially model dependent and is not based on

Positive Cosmological Constant and Quantum Theory

  • F. Lev
  • Physics, Mathematics
  • 2010
The cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli).

A Simple Proof That Finite Quantum Theory And Finite Mathematics Are More Fundamental Than Standard Quantum Theory And Classical Mathematics, Respectively

  • F. Lev
  • Mathematics, Philosophy
  • 2019
Standard quantum theory is based on classical mathematics involving such notions as infinitely small/large and continuity. Those notions were proposed by Newton and Leibniz more than 300 years ago

Could only fermions be elementary

In standard Poincare and anti de Sitter SO(2, 3) invariant theories, antiparticles are related to negative energy solutions of covariant equations while independent positive energy unitary

de Sitter symmetry and quantum theory

  • F. Lev
  • Physics, Mathematics
  • 2011
de Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental

Cosmological Acceleration as a Consequence of Quantum de Sitter Symmetry

  • F. Lev
  • Physics
    Physics of Particles and Nuclei Letters
  • 2020
Physicists usually understand that physics cannot (and should not) derive that $c\approx 3\cdot 10^8m/s$ and $\hbar \approx 1.054\cdot 10^{-34}kg\cdot m^2/s$. At the same time they usually believe



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