arXiv subjects

A. N. Tarakanov

Publications and source records attributed to A. N. Tarakanov.

4 recordsLinked to original sources

arXiv2012

Zitterbewegung as purely classical phenomenon

Nonrelativistic formalism is developed, which allows describing systems with internal degrees of freedom in the scalar potential field $U$, which is a function both on relative coordinates and time, and on relative speed and accelerations. The equation for energy, which is an integral of motion when $U$ satisfies to certain differential condition, is derived for the general case. For a free mass point all solutions of the equations of motion in the center-of-inertia reference frame, moving with constant velocity, are found. As a result, the center of mass follows along helical and more complicated trajectories round a direction of motion of the center of inertia. This motion can be interpreted as trembling movement (Zitterbewegung). On this basis a conclusion is done that Zitterbewegung has purely classical origin, arising even in a nonrelativistic case if internal degrees of freedom are taken into account. The general equation of motion for a spin which can be interpreted from positions of a classical mechanics is written down. Application of the obtained results to the electron leads to new conception of electric charge, sign of which corresponds to a sign of spin polarization.

physics.class-ph↗

arXiv2010

Generalized Dynamics of the Mass Point with Internal Degrees of Freedom

An equation of motion of the mass point with internal degrees of freedom in scalar potential $U$ depending on relative coordinates and time, velocity and accelerations is obtained both for non-relativistic and relativistic case. In non-relativistic case a generalization of the energy conservation law follows, if $\partial U / \partial t = 0$ fulfilled. A concept of work is generalized to relativistic case, leading to corresponding integral of motion, if $\partial U / \partial τ= 0$ fulfilled, where $τ$ is proper time of the point. In neglecting an internal degrees of freedom and absence of interaction this integral of motion gives standard Special Relativity.

hep-th↗

arXiv2007

On relativistic theory of spinning and deformable particles

A model of relativistic extended particle is considered with the help of generalization of space-time inter-val. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained 14-dimensional space is assumed to be an embedding one both for usual space-time and for 10-dimensional internal space of rotational and deformational variables. To describe such an internal space relativistic generaliza-tions of inertia and deformation tensors are given. Independence of internal and external motions from each other gives rise to splitting the equation of motion and some conditions for 14-dimensional metric. Using the 14-dimensional ideology makes possible to assign a unique proper time for all points of extended object, if the metric will be degenerate. Properties of an internal space are discussed in details in the case of absence of spatial rotations.

hep-th↗

arXiv2006

Homogeneous space-times as models for isolated extended objects

An extended object is considered on the Minkowski background in the form of a space-time bag, which is bounded by a certain surface confining an internal substance. An internal metric is built starting from the symmetry principles rather than from the field equations. Assuming such a surface to be Lorentz invariant we find that the internal space is proved to be the de Sitter space. Conformal inversion of the internal metric relative to the bag surface determines an external space (conformally conjugated de Sitter space) whose metric may simulate a field of the object. Although the extended object built in a such a way is noncompact, its cross section by the hyperplane r^0=0, where r^0 is the temporal coordinate, is compact (a ball) and the associated metric can model a spherically symmetric extended massless charge in a certain approximation.

hep-th↗