A. Tarakanov - Academia.edu (original) (raw)
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Papers by A. Tarakanov
The behavior of spinning particles in the stationary homogeneous magnetic field is considered and... more The behavior of spinning particles in the stationary homogeneous magnetic field is considered and all types of trajectories for massive and massless particles are found. It is shown that spin of particles in a magnetic field is always arranged parallel or antiparallel to the field. Helicity eee plays a role of electric charge. The oscillation frequency of massless particle in a magnetic field increases.
Theoretical and Mathematical Physics, 1976
ABSTRACT For a special choice of the parameter matrices, pseudo-orthogonal and pseudo-unitary tra... more ABSTRACT For a special choice of the parameter matrices, pseudo-orthogonal and pseudo-unitary transformations are represented in the form of polynomials of second degree in these matrices. The connection between the transformation parameters and generalized velocities in the case of subluminal and superluminal generalized velocities is established. The resulting transformations are a generalization of Lorentz transformations describing pure motion to arbitrary real and complex pseudo-Euclidean spaces. The law of composition of the generalized velocities is found.
International Journal of Theoretical Physics, 1984
A sigma model associated with the Ernst equation is derived. This sigma model is described by the... more A sigma model associated with the Ernst equation is derived. This sigma model is described by the Belinsky-Zakharov-type completely integrable equation and is formally equivalent to the usual sigma model in curved two-dimensional space. The corresponding Lax representation, BÄcklund transformation, and divergence-free currents are obtained.
arXiv: Classical Physics, 2015
By means of the method of moving Frenet-Serret frame the set of equations of motion is derived fo... more By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as well as by two pseudo-vectors one of which is easily associated with external magnetic field, and another still remains undetermined. The equations give a possibility to describe the motion of both massive and massless particles with spin. All solutions of the equations of motion in the absence of external fields were found, and besides, we give more precise definition of a free object. It turns out that the massive particles always possess a longitudinal polarization. There are possible transversal motions of the following types: 1) oscillatory motion with proper frequency, 2) circular motion, and 3) complicated motion along rosette trajectories round the center of inertia with the velocity, varying in finite limits. Free massless particles can ...
The behavior of spinning particles in the stationary homogeneous magnetic field is considered and... more The behavior of spinning particles in the stationary homogeneous magnetic field is considered and all types of trajectories for massive and massless particles are found. It is shown that spin of particles in a magnetic field is always arranged parallel or antiparallel to the field. Helicity plays a role of electric charge. The oscillation frequency of massless particle in a magnetic field increases.
The behavior of spinning particles in the stationary homogeneous electric field is considered and... more The behavior of spinning particles in the stationary homogeneous electric field is considered and trajectories are found for various spin orienta-tions. We study the acceleration of spinning particles by an electric field, as well as the electric and magnetic deflection in constant homogeneous fields. It is shown that the classical Lorentz-Einstein theory of motion of charged particles is a special case of the proposed theory.
The behavior of spinning particles in the stationary homogeneous magnetic field is considered and... more The behavior of spinning particles in the stationary homogeneous magnetic field is considered and all types of trajectories for massive and massless particles are found. It is shown that spin of particles in a magnetic field is always arranged parallel or antiparallel to the field. Helicity eee plays a role of electric charge. The oscillation frequency of massless particle in a magnetic field increases.
Theoretical and Mathematical Physics, 1976
ABSTRACT For a special choice of the parameter matrices, pseudo-orthogonal and pseudo-unitary tra... more ABSTRACT For a special choice of the parameter matrices, pseudo-orthogonal and pseudo-unitary transformations are represented in the form of polynomials of second degree in these matrices. The connection between the transformation parameters and generalized velocities in the case of subluminal and superluminal generalized velocities is established. The resulting transformations are a generalization of Lorentz transformations describing pure motion to arbitrary real and complex pseudo-Euclidean spaces. The law of composition of the generalized velocities is found.
International Journal of Theoretical Physics, 1984
A sigma model associated with the Ernst equation is derived. This sigma model is described by the... more A sigma model associated with the Ernst equation is derived. This sigma model is described by the Belinsky-Zakharov-type completely integrable equation and is formally equivalent to the usual sigma model in curved two-dimensional space. The corresponding Lax representation, BÄcklund transformation, and divergence-free currents are obtained.
arXiv: Classical Physics, 2015
By means of the method of moving Frenet-Serret frame the set of equations of motion is derived fo... more By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as well as by two pseudo-vectors one of which is easily associated with external magnetic field, and another still remains undetermined. The equations give a possibility to describe the motion of both massive and massless particles with spin. All solutions of the equations of motion in the absence of external fields were found, and besides, we give more precise definition of a free object. It turns out that the massive particles always possess a longitudinal polarization. There are possible transversal motions of the following types: 1) oscillatory motion with proper frequency, 2) circular motion, and 3) complicated motion along rosette trajectories round the center of inertia with the velocity, varying in finite limits. Free massless particles can ...
The behavior of spinning particles in the stationary homogeneous magnetic field is considered and... more The behavior of spinning particles in the stationary homogeneous magnetic field is considered and all types of trajectories for massive and massless particles are found. It is shown that spin of particles in a magnetic field is always arranged parallel or antiparallel to the field. Helicity plays a role of electric charge. The oscillation frequency of massless particle in a magnetic field increases.
The behavior of spinning particles in the stationary homogeneous electric field is considered and... more The behavior of spinning particles in the stationary homogeneous electric field is considered and trajectories are found for various spin orienta-tions. We study the acceleration of spinning particles by an electric field, as well as the electric and magnetic deflection in constant homogeneous fields. It is shown that the classical Lorentz-Einstein theory of motion of charged particles is a special case of the proposed theory.