Science Journals

All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident: Arthur Schopenhauer -- In questions of science the authority of a thousand is not worth the humble reasoning of a single individual: Galileo Galilei -- Science is a wonderful thing if one does not have to earn one's living at it: Albert Einstein -- When you have eliminated the impossible, what ever remains, however improbable must be the truth: Sir Arthur Conan Doyle -- We all agree that your theory is crazy, but is it crazy enough? Niels Bohr -- Whenever a true theory appears, it will be its own evidence. Its test is that it will explain all phenomena: Ralph Waldo Emerson -- Since the mathematicians invaded Relativity, I do not understand it myself anymore: Albert Einstein -- I would say that the aether is a medium invented by man for the purpose of propagating his misconceptions from one place to another: W.F.G. Swann: -- Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone: Albert Einstein -- Physics is mathematical not because we know so much about the physical world, but because we know so little: Bertrand Russell -- If I could explain it to the average person, I would not have been worth the Nobel Prize: R. P. Feynman -- I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use: Galileo Galilei -- How dare we speak of the laws of chance? Is not chance the antithesis of all law?: Bertrand Russell -- Only two things are infinite, the universe and human stupidity, and I´m not sure about the former: Albert Einstein -- The glory of mathematics is that you don't have to say what you are talking about: Richard Feynman -- Anything is possible if you don´t know what you are talking about: Author Unknown -- In life, everything is relative - except Einstein´s theory: Leonid S. Sukhorukov -- Don´\'t worry about people stealing your ideas. If your ideas are any good, you´ll have to ram them down people´s throats: Howard Aiken --A day will come undoubtedly when the ether will be discarded as useless: H. Poincaré -- First they tell you you´re wrong and they can prove it; then they tell you you´re right but it isn´t important; then they tell you it´s important but they knew it all along: Charles Kettering -- It is not once nor twice but times without number that the same ideas make their appearance in the world: Aristotle -- The opposite of a true statement is a false statement. The opposite of a profound truth may well be another profound truth: Niels Bohr -- A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it: Max Planck -- Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions: Eric Temple Bell -- Half this game is ninety percent mental: Yogi Berra

A Set-Matrix Duality Principle for the Dirac Equation

Author:

Sharafiddinov, Rasulkhozha Sultonkhozhaevich

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

December 4, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10384

Downloads:

214

Keywords:

real space, imaginary space, regular matrices, casual matrices, real number axis, imaginary number axis, an empty matrix, a set-matrix duality, matrix operations, set operations

Abstract:

Spontaneous mirror symmetry violation is carried out in nature as the transition between the usual left (right)-handed and the mirror right (left)-handed spaces, in each of which the usual and mirror particles have the diﬀerent lifetimes. As a consequence, all equations of motion in a uniﬁed ﬁeld theory of elementary particles include the mass, energy and momentum as the matrices expressing the ideas of the left- and right-handed neutrinos are of long- and short-lived objects, respectively. These ideas require in principle to go away from the chiral deﬁnitions of the structure of matter ﬁelds taking into account that the Dirac matrices are, in the Weyl presentation, reduced to the matrices indicating to the absence in nature of a place for parity conservation but not allowing to follow the dynamical origination of its spontaneous violation. We discuss a theory in which a set comes forward at the new level, namely, at the level of set-matrix duality principle as a criterion for matrices. This connection gives the exact mathematical deﬁnitions of internally disclosed and undisclosed matrices, allowing to formulate three more deﬁnitions, three lemmas and two pairs of axioms. Thereby, it involves that there is no single matrix, for which an absolutely empty matrix would not exist. The sets of matrix elements and the matrices of set elements thus found unite all of matrix and set operations necessary for deciding the problems in a uniﬁed whole.

<<< Back