Clifford algebra in classical electrodynamical hydrogen atom model

Simulik, V. M.; Krivsky, I.Yu.

doi:10.1007/bf03041213

Cited by 10 publications

(13 citation statements)

References 4 publications

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“…What is the meaning of these equations in physics? To answer these questions one can be referred to our pal~ers [24][25][26][27][28][29]32], where (i) using the solutions of these equations the speculation about the existence of longitudinal electromagnetic waves near the gradient-like currents and charges was suggested, (ii) on the basis of these equations the hydrogen spectrum was described completely within the framework of a classical electrodynamics without any appealing to probabilities and quantum mechanics (see also the review in [33]). Other, related, analysis of the massless Dirac to Maxwell equations can be found in the interesting approach of Vaz, Rodrigues et al [34][35][36][37][38].…”

Section: Discussionmentioning

confidence: 99%

Bosonic symmetries of the massless Dirac equation

Simulik

Krivsky

1998

AACA

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The results of spin 1 symmetries of massless Dirac equation [21] ate proved completely in the space of 4-component Dirac spinors on the basis of unitary operator in this space connecting this equation with the Maxwell equations containing gradient-like sources. Nonlocal representations of conformal group are found, which generate the transformations leaving the massless Dirac equation being invariant. The Maxwell equations with gradient-like sources are proved to be invariant with respect to fermionic representations of Poincar› and conformal groups and to be the kind of Maxwell equations with maximally symmetrical properties. Brief consideration of an application of these equations in physics is discussed. I n t r o d u c t i o nThe relationship between the massless Dirac equation and the Maxwell equations is a subject of interest of investigators since the time of creation of quantum mechanics. In [10,13,15,16] one can find the beginning of investigation of the most interesting case where the mass is nonzero and the interaction

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Section: Discussionmentioning

confidence: 99%

Bosonic symmetries of the massless Dirac equation

Simulik

Krivsky

1998

AACA

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“…1 0 0 0 0 −1 0 0 0 0 −1 0 0 0 0 1 (31) rather than in the canonical field theory form (25). The statistical sense of the amplitudes is conserved in…”

Section: The Fermi-bose Duality and The Fermi-bose Statisticsmentioning

confidence: 99%

“…In another approach [24][25][26][27][28][29][30], the quadratic relations between the fermionic and bosonic amplitudes were found and applied. In our papers [3][4][5][6][7][21][22][23] and herein we discuss the linear relations between fermionic and bosonic amplitudes.…”

Section: Introductionmentioning

confidence: 99%

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Some statistical aspects of the spinor field Fermi-Bose duality

Simulik¹,

Krivsky²,

Lamer³

2012

Condens. Matter Phys.

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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.

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“…In our long-term investigations of the mapping of the Maxwell theory on the Dirac theory, we also studied the different exotic representations of the Clifford-Dirac algebra, which were useful in the description of the Maxwell theory in the notations taking from the formalism of the Dirac spinor field (see, e.g., [14] and [15]).…”

Section: Briefly On the Gamma Matrix Representations Of The Real Clifmentioning

confidence: 99%

Symmetries of Relativistic Hydrogen Atom

Simulik

Gordievich²

2019

Ukr. J. Phys.

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The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above-mentioned algebras commute with the operator of the Dirac equation in an external Coulomb field and, therefore, determine the algebras of invariance of such Dirac equation. Hence, the spin s = (1, 0) Bose symmetry of the Dirac equation for the free spinor field, proved recently in our papers, is extended here for the Dirac equation interacting with an external Coulomb field. A relativistic hydrogen atom is modeled by such Dirac equation. We are able to prove for the relativistic hydrogen atom both the fermionic and bosonic symmetries known from our papers in the case of a non-interacting spinor field. New symmetry operators are found on the basis of new gamma matrix representations of the Clifford and SO(8) algebras, which are known from our recent papers as well. Hidden symmetries were found both in the canonical Foldy–Wouthuysen and covariant Dirac representations. The found symmetry operators, which are pure matrix ones in the Foldy–Wouthuysen representation, become non-local in the Dirac model.

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Clifford algebra in classical electrodynamical hydrogen atom model

Cited by 10 publications

References 4 publications

Bosonic symmetries of the massless Dirac equation

Bosonic symmetries of the massless Dirac equation

Some statistical aspects of the spinor field Fermi-Bose duality

Symmetries of Relativistic Hydrogen Atom

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