A Set-Matrix Duality Principle for the Dirac Equation
Poster-In-person · Withdrawn
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 [1,2] 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
$$\alpha= {{0 \ \, \, \, \, \sigma}\choose{\sigma \, \, \, \, \ 0}}, \, \, \, \,
\beta={{I \ \, \, \, \, \ 0}\choose{0 \ -I}}, \, \, \, \,
\gamma_{5}={{0 \, \, \, \, \ I}\choose{I \ \, \, \, \, \ 0}}$$
including a unity $I$ matrix, the Pauli spin $\sigma$ matrices are, in the Weyl presentation, reduced to the matrices
$$\alpha= {{\sigma \ \, \, \, \, \ 0}\choose{0 \, \, \, \, -\sigma}}, \, \, \, \,
\beta={{0 \, \, \, \, \ I}\choose{I \ \, \, \, \, \ 0}}, \, \, \, \,
\gamma_{5}={{I \ \, \, \, \, \ 0}\choose{0 \ -I}}
\eqno(1)$$
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 expresses in whole the idea of a kind of system of matrices from
$$\alpha={{\sigma \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ \sigma}}, \, \, \, \,
\beta={{0 \, \, -I}\choose{I \ \, \, \, \, \ 0}}, \, \, \, \,
\gamma_{5}={{I \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ I}},$$
$$\alpha={{\sigma \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ \sigma}}, \, \, \, \,
\beta={{\ 0 \ \, \, \, \, \ I}\choose{-I \ \, \, \, \, \ 0}}, \, \, \, \,
\gamma_{5}={{I \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ I}},$$
each of which is unlike (1) a fully regular presentation of Dirac matrices.
$$\alpha= {{0 \ \, \, \, \, \sigma}\choose{\sigma \, \, \, \, \ 0}}, \, \, \, \,
\beta={{I \ \, \, \, \, \ 0}\choose{0 \ -I}}, \, \, \, \,
\gamma_{5}={{0 \, \, \, \, \ I}\choose{I \ \, \, \, \, \ 0}}$$
including a unity $I$ matrix, the Pauli spin $\sigma$ matrices are, in the Weyl presentation, reduced to the matrices
$$\alpha= {{\sigma \ \, \, \, \, \ 0}\choose{0 \, \, \, \, -\sigma}}, \, \, \, \,
\beta={{0 \, \, \, \, \ I}\choose{I \ \, \, \, \, \ 0}}, \, \, \, \,
\gamma_{5}={{I \ \, \, \, \, \ 0}\choose{0 \ -I}}
\eqno(1)$$
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 expresses in whole the idea of a kind of system of matrices from
$$\alpha={{\sigma \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ \sigma}}, \, \, \, \,
\beta={{0 \, \, -I}\choose{I \ \, \, \, \, \ 0}}, \, \, \, \,
\gamma_{5}={{I \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ I}},$$
$$\alpha={{\sigma \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ \sigma}}, \, \, \, \,
\beta={{\ 0 \ \, \, \, \, \ I}\choose{-I \ \, \, \, \, \ 0}}, \, \, \, \,
\gamma_{5}={{I \ \, \, \, \, \ 0}\choose{0 \ \, \, \, \, \ I}},$$
each of which is unlike (1) a fully regular presentation of Dirac matrices.
–
· 291 Publication: 1. R.S. Sharafiddinov, Can. J. Phys. 93 (2015) 10, 1005-1008.
Available from: https://doi.org//10.1139/cjp-2014-0497.
2. R.S. Sharafiddinov, Int. J. Theor. Phys. 55 (2016) 4, 2139-2147.
Available from: https://doi.org/10.1007/s10773-015-2852-3.
Presenters
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Rasulkhozha Sharafiddinov
- Institute of Nuclear Physics, Uzbekistan Academy of Sciences