arXiv subjects

V. M. Simulik

Publications and source records attributed to V. M. Simulik.

14 recordsLinked to original sources

arXiv2024

The Dirac Equation Near Centenary: a Contemporary Introduction to the Dirac Equation Consideration

More then 35 approaches to the Dirac equation derivation are presented. The various physical principles and mathematical methods are used. A review of well-known and not enough known contributions to the problem is given, the unexpected and unconventional derivations are presented as well. Three original approaches to the problem suggested by the author are considered as well. They are (i) the generalization of H. Sallhofer derivation, (ii) the obtaining of the massless Dirac equation from the Maxwell equations in maximally symmetrical form, (iii) the derivation of the Dirac equation with nonzero mass from the relativistic canonical quantum mechanics of the fermion-antifermion spin s=1/2 doublet. Today we are able to demonstrate new features of our derivations given in original papers. In some sense the important role of the Dirac equation in contemporary theoretical physics is demonstrated. A criterion for the usefulness of one or another derivation of the Dirac equation has been established

math-ph↗

arXiv2023

On the 256-dimensional gamma matrix representation of the Clifford algebra Cl(1,7) and its relation to the Lie algebra SO(1,9)

Extended gamma matrix Clifford--Dirac and SO(1,9) algebras in the terms of $8 \times 8$ matrices have been considered. The 256-dimensional gamma matrix representation of Clifford algebra for 8-component Dirac equation is suggested. Two isomorphic realizations $\textit{C}\ell^{\texttt{R}}$(0,8) and $\textit{C}\ell^{\texttt{R}}$(1,7) are considered. The corresponding gamma matrix representations of 45-dimensional SO(10) and SO(1,9) algebras, which contain standard and additional spin operators, are introduced as well. The SO(10), SO(1,9) and the corresponding $\textit{C}\ell^{\texttt{R}}$(0,8)$, \textit{C}\ell^{\texttt{R}}$(1,7) representations are determined as algebras over the field of real numbers. The suggested gamma matrix representations of the Lie algebras SO(10), SO(1,9) are constructed on the basis of the Clifford algebras $\textit{C}\ell^{\texttt{R}}$(0,8)$, \textit{C}\ell^{\texttt{R}}$(1,7) representations. Comparison with the corresponded algebras in the space of standard 4-component Dirac spinors is demonstrated. The proposed mathematical objects allow generalization of our results, obtained earlier for the standard Dirac equation, for equations of higher spin and, especially, for equations, describing particles with spin 3/2. The maximal 84-dimensional pure matrix algebra of invariance of the 8-component Dirac equation in the Foldy--Wouthuysen representation is found. The corresponding symmetry of the Dirac equation in ordinary representation is found as well. The possible generalizations of considered Lie algebras to the arbitrary dimensional SO(n) and SO(m,n) are discussed briefly.

physics.gen-ph↗

arXiv2022

On the "old" and "new" relativistic wave equations for the particle having spin s=3/2

Relativistic wave equation of motion without redundant components for the particle having spin 3/2 has been considered. In order to show the newness a comparison with the known equations for the spin s=3/2 field is given. Therefore, the brief review of the relativistic wave equations for the particle with spin s=3/2 is given. In our equation the wave function for the particle-antiparticle doublet has only 8 components. The consideration is carried out both at the level of relativistic quantum mechanics and at the level of local field theory. The extended Foldy--Wouthuysen transformation, which gives the operator link between these two levels is suggested.

hep-th↗

arXiv2021

Extended real Clifford-Dirac algebra and bosonic symmetries of the Dirac equation with nonzero mass

Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional gamma matrix representations of the Clifford algebra and corresponding representations of SO(10) and SO(1,9) algebras over the field of real numbers are introduced. This turned out to be possible in the space of eight-component spinors, and not for the ordinary four-component Dirac spinors. The proposed mathematical objects allow the generalization of our results, obtained earlier for the standard Dirac equation, for the equations of higher spin and, especially, for the equations, describing the particles with spin 3/2.

math-ph↗

arXiv2020

Longitudinal electromagnetic waves in the framework of standard classical electrodynamics

Theoretical comment for the registration of longitudinal electric waves in interacting laser beams is given. Recent information on longitudinal electric and scalar waves in plasma, plasmons, waveguides, antennas and nano-structures is considered. The link between the longitudinal electromagnetic waves and the system of Maxwell equations is demonstrated. The longitudinal wave component of the electric field strength vector is found as the exact solution of the standard Maxwell equations with specific gradient-type case of electric current and charge densities. The corresponded scalar wave is found as well. The necessary comment on the paper of K.J. van Vlaenderen and A. Waser is given. The possible experimental situation is discussed briefly. Following the Bialynicki-Birula's proposition to give the name for the well known complex 3-vector of electromagnetic field strengths, the suggestion to call the much more interesting 4-vector of this kind as Riemann--Silberstein--Darwin vector is given.

physics.class-ph↗

arXiv2017

Calculations for electron-impact ionization of magnesium and calcium atoms in the method of interacting configurations in the complex number representation

Next investigations in our program of transition from the He atom to the complex atoms description have been presented. The method of interacting configurations in the complex number representation is under consideration. The spectroscopic characteristics of the Mg and Ca atoms in the problem of the electron-impact ionization of these atoms are investigated. The energies and the widths of the lowest autoionizing states of Mg and Ca atoms are calculated. Few results in the photoionization problem on the autoionizing states above the n=2 threshold of helium-like Be ion are presented.

physics.atom-ph↗

arXiv2016

Calculations for electron-impact ionization of beryllium in the method of interacting configurations in the complex number representation

The beginning of the application of the method of interacting configurations in the complex number representation to the compound atomic systems has been presented. The spectroscopic characteristics of the Be atom in the problem of the electron-impact ionization of this atom are investigated. The energies and the widths of the lowest autoionizing states of Be atom are calculated.

physics.atom-ph↗

arXiv2015

General form of the covariant field equations of arbitrary spin and the relativistic canonical quantum mechanics

The investigation of arXiv 1409.2766v2 [quant-ph] has been continued by the general form of the numerous equations with partial values of arbitrary spin, which were considered in above mentioned preprint. The general forms of quantum-mechanical and covariant equations for arbitrary spin together with the general description of the arbitrary spin field formalism are presented. The corresponding relativistic quantum mechanics of arbitrary spin is given as the system of axioms. Previously ignored partial example of the spin s=(0,0) particle-antiparticle doublet is considered. The partial example of spin s=(3/2,3/2) particle-antiparticle doublet is highlighted. The new 64 dimensional Clifford--Dirac algebra over the field of real numbers is suggested. The general operator, which transformed the relativistic canonical quantum mechanics of arbitrary spin into the locally covariant field theory, has been introduced. Moreover, the study of the place of the results given in arXiv 1409.2766v2 [quant-ph] among the results of other authors is started. The review of the different investigations in the area of relativistic canonical quantum mechanics is given and the brief analysis of the existing approaches to the covariant field theory of arbitrary spin is initiated. The consideration of some important details of arXiv 1409.2766v2 [quant-ph] is improved.

quant-ph↗

arXiv2013

Structure and different realizations of the extended real Clifford-Dirac algebra

The structure of the 64-dimensional extended real Clifford-Dirac (ERCD) algebra, which has been introduced in our paper Phys. Lett. A. 375 (2011) 2479, is under consideration. The subalgebras of this algebra are investigated: the 29-dimensional proper ERCD algebra and 32-dimensional pure matrix algebra of invariance of the Dirac equation in the Foldy-Wouthuysen representation. The last one is the maximal pure matrix algebra of invariance of this equation. The different realizations of the proper ERCD algebra are given. The application of proper ERCD algebra is illustrated on the example of the derivation of the hidden spin (1,0) Poincare symmetry of the Dirac equation.

math-ph↗

arXiv2013

The Schrodinger-Foldy relativistic canonical quantum mechanics and the derivation of the Dirac equation

The detailed consideration of the relativistic canonical quantum-mechanical model of an arbitrary spin-multiplet is given. The group-theoretical analysis of the algebra of experimentally observables physical quantities for the spin 1/2 doublet is presented. It is shown that both the Foldy-Wouthuysen equation for the fermionic spin 1/2 doublet and the Dirac equation in its local representation are the consequences of the relativistic canonical quantum mechanics of the corresponding doublet. The mathematically well-defined consideration on the level of modern axiomatic approaches to the field theory is provided. The hypothesis of the antiparticle negative mass is discussed briefly in the section conclusions.

math-ph↗

arXiv2012

Some statistical aspects of the spinor field Fermi-Bose duality

The structure of 29-dimensional extended real Clifford-Dirac algebra, which has been introduced in our paper Phys. Lett. A, 2011, 375, 2479, is considered in brief. Using this algebra, the property of Fermi-Bose duality of the Dirac equation with nonzero mass is proved. It means that Dirac equation can describe not only the fermionic but also the bosonic states. The proof of our assertion based on the examples of bosonic symmetries, solutions and conservation laws is given. Some statistical aspects of the spinor field Fermi-Bose duality are discussed.

math-ph↗

arXiv2011

On Bosnic Solutions of the Foldy-Wouthuysen and Dirac Equations for Free Field

The consideration of the Fermi - Bose duality of the Dirac equation with arbitrary mass has been continued. The bosonic solutions of this equation in the Foldy - Wouthuysen representation are found. The Bargman - Wigner analysis of additional solutions and comparison with standard fermionic solutions are carried out. The evident demonstration of additional bosonic features of the Foldy - Wouthuysen and Dirac equation is presented.

math-ph↗

arXiv2010

On the Fermi - Bose duality of the Dirac equation with nonzero mass

We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2, but also bosons of spin 1. The new bosonic symmetries of the Dirac equation in both the Foldy -- Wouthuysen and the Pauli -- Dirac representations are found. Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance) the new, physically meaningful spin 1 Poincare symmetry of equation under consideration is proved. In order to carry out the corresponding proofs a 64-dimensional extended real Clifford -- Dirac algebra is put into consideration.

math-ph↗

arXiv2002

Slightly generalized Maxwell classical electrodynamics can be applied to inneratomic phenomena

In order to extend the limits of classical theory application in the microworld some weak generalization of Maxwell electrodynamics is suggested. It is shown that slightly generalized classical Maxwell electrodynamics can describe the intraatomic phenomena with the same success as relativistic quantum mechanics can do. Group-theoretical grounds for the description of fermionic states by bosonic system are presented briefly. The advantages of generalized electrodynamics in intraatomic region in comparison with standard Maxwell electrodynamics are demonstrated on testing example of hydrogen atom. We are able to obtain some results which are impossible in the framework of standard Maxwell electrodynamics. The Sommerfeld - Dirac formula for the fine structure of the hydrogen atom spectrum is obtained on the basis of such Maxwell equations without appealing to the Dirac equation. The Bohr postulates and the Lamb shift are proved to be the consequences of the equations under consideration. The relationship of the new model with the Dirac theory is investigated. Possible directions of unification of such electrodynamics with gravity are mentioned.

hep-th↗