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On Symmetry Properties of Quaternionic Analogs of Julia Sets
By means of theory group analysis, some algebraic and geometrical properties of quaternion analogs of \emph{Julia} sets are investigated. We argue that symmetries, intrinsic to quaternions, give riseExpand
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Symmetry properties of quaternionic and biquaternionic analogs of Julia sets
The symmetries intrinsic to quaternions and biquaternions give rise to a class of identical Julia sets, which does not exist in the complex number case. In the case of quadratic mapping X k + 1 = eXExpand
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Schr\"{o}dinger particle in magnetic and electric fields in Lobachevsky and Riemann spaces
Schr\"{o}dinger equation in Lobachevsky and Riemann 4-spaces has been solved in the presence of external magnetic field that is an analog of a uniform magnetic field in the flat space. GeneralizedExpand
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Duffin-Kemmer-Petiau formalism reexamined: non-relativistic approximation for spin 0 and spin 1 particles in a Riemannian space-time
It is shown that the generally covariant Duffin-Kemmer-Petiau equation, formulated in the frame of the Tetrode-Weyl-Fock-Ivanenko tetrad formalism, allows for a non-relativistic approximation if theExpand
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Maxwell equations in complex form of Majorana–Oppenheimer, solutions with cylindric symmetry in Riemann S3 and Lobachevsky H3 spaces
Complex formalism of Riemann–Silberstein–Majorana–Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe ofExpand
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Green function renormalization in SU(2)L ⊗ U(1) four-fermion model
Using the Dyson-Schwinger equation, the four-fermion Green functions in one-loop approximation to the SU(2)L ⊗ U(1) four-fermion model are found, as well as corrections to them. An expression isExpand
Cayley–Dickson Procedure, Relativistic Wave Equations and Supersymmetric Oscillators
The relativistic first-order wave equations for massive particles with spin 0,1,1/2 are formulated in terms of a factorization of the Klein–Fock equation by means of the algebra of octonions. AnExpand
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Spin 1 Particle in a 15-Component Formalism, Interaction with Electromagnetic and Gravitational Fields
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated.Expand