arXiv subjects

S. S. Sannikov

Publications and source records attributed to S. S. Sannikov.

4 recordsLinked to original sources

arXiv1999

Elementary Particles in a New Quantum Scheme

Proceeding from the main principles of the non-unitary quantum theory of relativistic bi-Hamiltonian systems, a system of Lagrangian fields characterized by a certain dispersion law (mass spectrum of particles), interactions between them and their coupling constants are constructed. In this article the mass spectrum formula for ``bare'' fundamental hadrons is introduced, and an a priori normalization of particle fields is found as well. Numerical values of some parameters of the present theory are determined.

quant-ph↗

arXiv1998

Quantization of the Dirac Fibre: a New Way in the Particle Physics

The problem of ultraviolet divergences is analysed in the quantum field theory. It was found that it has common roots with the problem of cosmological singularity. In the context of fibre bundles the second quantization method is represented as a procedure of the quantization for vector bundle cross-section. It is shown to be quite a different quantization way called as a fibre quantization which leads to an idea on existence of the non-standard dynamical system, i.e. the relativistic be-Hamiltonian system. It takes place on supersmall distances and is well described by the mathematical apparatus for the non-unitary quantum scheme using a dual pair of topological vector spaces in terms of the non-Hermitian form. The article contains the proof of the theorem on radical changes in space and in matter structure taking place for a very high density of matter: the phase transitions ``Lagrangian field system (elementary particles) $\to$ relativistic bi-Hamiltonian system (Feynman's partons)'' and ``continuum $\to$ discontinuum''. All required calculations in the framework of the proposed theory are published in the Russian periodicals. The purpose of this article is to replace the calculations by reasonings and concepts. The present article begins the systematic exposition of principles of the theory.

quant-ph↗

arXiv1998

Non-Fock Representations of Heisenberg Algebras

The purpose of this paper is to present the mathematical techniques of a new quantum scheme using a dual pair of reflexive topological vector spaces in terms of the non-Hermitian form. The scheme is shown to be a generalization of the well-known unitary quantum theory and to describe jointly quantum objects and physical vacuum.

quant-ph↗

arXiv1998

Charge Renormalization in a New Kind of Non-Local Quantum Electrodynamics

The goal of this message is to calculate radiative corrections to the Sommerfeld fine structure constant in the framework of a new QED in which particles are described by bilocal fields. The bare constant is 1/136 where 136 is a dimension of the dynamical group of the bihamiltonian system underlying the suggested elementary particle theory. Our calculations in the second order of perturbation theory give the renormalized Sommerfeld constant 1/137.0345. We believe the difference (137.0359 - 137.0345) between corresponding experimental and theoretical values may be understood as corrections of the fourth order.

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