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Alexei A. Deriglazov

Publications and source records attributed to Alexei A. Deriglazov.

At least 37 records · Page 2Linked to original sources
arXiv2021

Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime

We present the manifestly covariant Lagrangian of a massless polarized particle, that implies all dynamic and algebraic equations as the conditions of extreme of this variational problem. The model allows for minimal interaction with a gravitational field, leading to the equations, coinciding with Maxwell equations in the geometrical optics approximation. The model allows also a wide class of non minimal interactions, which suggests an alternative way to study the electromagnetic radiation beyond the leading order of geometrical optics. As a specific example, we construct a curvature-dependent interaction in Schwarzschild spacetime, predicting the Faraday rotation of polarization plane, linearly dependent on the wave frequency. As a result, the Schwarzschild spacetime generates a kind of angular rainbow of light: waves of different frequencies, initially linearly-polarized in one direction, acquire different orientations of their polarization planes when propagate along the same ray.

gr-qc↗
arXiv2020

Nonminimal spin-field interaction of the classical electron and quantization of spin

I shortly describe semi-classical models of spinning electron and list a number of theoretical issues where these models turn out to be useful, see arXiv:1710.07135 for details. Then I discuss the possibility to extend the range of applicability of these models by introducing an interaction, that forces the spin to align up or down relative to its precession axis.

quant-ph↗
arXiv2019

Covariant version of Pauli Hamiltonian, spin-induced non commutativity, Thomas precession and precession of spin

We show that there is a manifestly covariant version of the Pauli Hamiltonian with equations of motion quadratic on spin and field strength. Relativistic covariance inevitably leads to noncommutative positions: classical brackets of the position variables are proportional to the spin. It is the spin-induced noncommutativity that is responsible for transforming the covariant Hamiltonian into the Pauli Hamiltonian, without any appeal to the Thomas precession formula. The Pauli theory can be thought to be $1/c^2$ approximation of the covariant theory written in special variables. These observations clarify the long standing question on the discrepancy between the covariant and Pauli Hamiltonians. We also discuss the transformational properties of spin axis in the passage from laboratory to comoving and instantaneous frames, and reveal the role of Thomas spin-vector in the covariant scheme.

physics.gen-ph↗
arXiv2019

Acceleration of particles in Schwarzschild and Kerr geometries

The Landau-Lifshitz decomposition of spacetime, or (1+3)-split, determines the three-dimensional velocity and acceleration as measured by static observers. We use these quantities to analyze the geodesic particles in Schwarzschild and Kerr spacetimes. We show that in both cases there is no room for a positive acceleration (repulsion). We also compute the escape and terminal speeds. The escape speed in the case of a static black hole coincides with the Newton result. For the Kerr spacetime, the escape speed depends on the polar angle, showing that a particle needs less energy to escape in the direction close to the polar axis. The terminal speed at the Schwarzschild horizon and at the Kerr ergosphere turns out to be equal to the speed of light. For a local, stationary observer near to a massive particle in geodesic motion on the equatorial plane of the Kerr spacetime, the analysis of the velocity reveals that such a particle never reaches the ergosphere. And, in the case of the Schwarzschild spacetime, we found that the geodesic trajectories reach the horizon perpendicularly.

gr-qc↗
arXiv2018

Frame-dragging effect in the field of non rotating body due to unit gravimagnetic moment

Nonminimal spin-gravity interaction through unit gravimagnetic moment leads to modified Mathisson-Papapetrou-Tulczyjew-Dixon equations with improved behavior in the ultrarelativistic limit. We present exact Hamiltonian of the resulting theory and compute an effective $\frac{1}{c^2}$\,-Hamiltonian and leading post-Newtonian corrections to the trajectory and spin. Gravimagnetic moment causes the same precession of spin ${\bf S}$ as a fictitious rotation of the central body with angular momentum ${\bf J}=\frac{M}{m}{\bf S}$. So the modified equations imply a number of qualitatively new effects, that could be used to test experimentally, whether a rotating body in general relativity has null or unit gravimagnetic moment.

gr-qc↗
arXiv2017

Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity

We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: A) One-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic {\it Zitterbewegung}; B) Spin-induced non commutativity and the problem of covariant formalism; C) Three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; D) Paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultra relativistic limit, and equations with improved behavior.

gr-qc↗
arXiv2017

Relativistic effects due to gravimagnetic moment of a rotating body

We compute exact Hamiltonian (and corresponding Dirac brackets) for spinning particle with gravimagnetic moment $κ$ in an arbitrary gravitational background. $κ=0$ corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. $κ=1$ leads to modified MPTD equations with reasonable behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. Rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with MPTD body: A) If a number of gyroscopes with various rotation axes are freely traveling together, the angles between the axes change with time. B) For specific binary systems, gravimagnetic moment gives a contribution to frame-dragging effect with the magnitude, that turns out to be comparable with that of Schiff frame dragging.

gr-qc↗
arXiv2016

Relativistic corrections to the algebra of position variables and spin-orbital interaction

In the framework of vector model of spin, we discuss the problem of a covariant formalism \cite{Pomeranskii1998} concerning the discrepancy between relativistic and Pauli Hamiltonians. We show how the spin-induced non commutativity of a position accounts the discrepancy on the classical level, without appeal to the Dirac equation and Foldy-Wouthuysen transformation.

quant-ph↗
arXiv2016

Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in ultra-relativistic regime and gravimagnetic moment

Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equations instead of the original metric $g$ emerges spin-dependent effective metric $G=g+h(S)$. So we need to decide, which of them the MPTD particle sees as the space-time metric. We show that MPTD equations, if considered with respect to original metric, have unsatisfactory behavior: the acceleration in the direction of velocity grows up to infinity in the ultra-relativistic limit. If considered with respect to $G$, the theory has no this problem. But the metric now depends on spin, so there is no unique space-time manifold for the Universe of spinning particles: each particle probes his own three-dimensional geometry. This can be improved by adding a non-minimal interaction of spin with gravity through gravimagnetic moment. The modified MPTD equations with unit gravimagnetic moment have reasonable behavior within the original metric.

gr-qc↗
arXiv2016

Ultra-relativistic spinning particle and a rotating body in external fields

We use the vector model of spinning particle to analyze the influence of spin-field coupling on the particle's trajectory in ultra-relativistic regime. The Lagrangian with minimal spin-gravity interaction yields the equations equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations of a rotating body. We show that they have unsatisfactory behavior in the ultra-relativistic limit. In particular, three-dimensional acceleration of the particle increases with velocity and becomes infinite in the ultra-relativistic limit. The reason is that in the equation for trajectory emerges the term which can be thought as an effective metric generated by the minimal spin-gravity coupling. Therefore we examine the non-minimal interaction through the gravimagnetic moment $κ$, and show that the theory with $κ=1$ is free of the problems detected in MPTD-equations. Hence the non-minimally interacting theory seem more promising candidate for description of a relativistic rotating body in general relativity. The Lagrangian for the particle in an arbitrary electromagnetic field in Minkowski space leads to generalized Frenkel and Bargmann-Michel-Telegdi equations. The particle with magnetic moment in electromagnetic field and the particle with gravimagnetic moment in gravitational field have very similar structure of equations of motion. In particular, the spin-electromagnetic coupling also produces an effective metric for the particle with anomalous magnetic moment. If we use the usual special-relativity notions for time and distance, then the critical speed, which the particle cannot exceed during its evolution in electromagnetic field, is different from the speed of light. This can be corrected assuming that the three-dimensional geometry should be defined with respect to the effective metric.

gr-qc↗
arXiv2016

Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations

We obtain Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body with given values of spin and momentum starting from Lagrangian action without auxiliary variables. MPTD-equations correspond to minimal interaction of our spinning particle with gravity. We shortly discuss some novel properties deduced from the Lagrangian form of MPTD-equations: emergence of an effective metric instead of the original one, non-commutativity of coordinates of representative point of the body, spin corrections to Newton potential due to the effective metric as well as spin corrections to the expression for integrals of motion of a given isometry.

gr-qc↗
arXiv2014

Lagrangian for Frenkel electron and position's non-commutativity due to spin

We construct relativistic-invariant spinning-particle Lagrangian without auxiliary variables. Spin is considered as a composed quantity constructed on the base of non-Grassmann vector-like variable. The variational problem guarantees both fixed value of spin and Frenkel condition on spin-tensor. Taking into account the Frenkel condition, we obtain, inevitably, relativistic corrections to the algebra of position variables: their classical brackets became noncommutative, with the "parameter of non-commutativity" proportional to the spin-tensor. This leads to a number of interesting consequences in quantum theory. We construct the relativistic quantum mechanics in canonical formalism (in physical-time parametrization) and in covariant formalism (in arbitrary parametrization). We show how state-vectors and operators of covariant formulation can be used to compute mean values of physical operators of position and spin. This proves relativistic covariance of canonical formalism. Various candidates for position and spin operators of an electron acquire clear meaning and interpretation in the Lagrangian model of Frenkel electron. We also establish the relation between Frenkel electron and positive-energy sector of Dirac equation, this allowed us to turn to the long-standing problem on spin and position operators of Dirac theory. Contrary to widely assumed opinion, our results argue in favor of Pryce's (d)-type operators. This implies that effects of non-commutativity could be presented at the Compton wave length, in contrast to conventional expectations at the Planck length. At last, we present the manifestly covariant form of spin and position operators of Dirac equation.

hep-th↗
arXiv2014

Lagrangian for the Frenkel electron

We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel and BMT equations to the case of an arbitrary electromagnetic field. For a particle with anomalous magnetic moment, singularity in the relativistic equations generally occurs at the speed different from the speed of light. Detailed discussion of the ultra-relativistic motion is presented in the work: A. A. Deriglazov and W. G. Ramirez, World-line geometry probed by fast spinning particle, arXiv:1409.4756.

physics.gen-ph↗
arXiv2014

World-line geometry probed by fast spinning particle

Interaction of spin with electromagnetic field yields an effective metric along the world line of spinning particle. If we insist to preserve the usual special-relativity definitions of time and distance, critical speed which spinning particle can not overcome during its evolution in external field differs from the speed of light. Instead, we can follow the general-relativity prescription to define physical time and distance in the presence of electromagnetic field. With these definitions, critical speed coincides with the speed of light. Effective metric arises also when spin interacts with gravitational field.

physics.gen-ph↗
arXiv2014

Frenkel electron on an arbitrary electromagnetic background and magnetic Zitterbewegung

We present Lagrangian which implies both necessary constraints and dynamical equations for position and spin of relativistic spin one-half particle. The model is consistent for any value of magnetic moment $μ$ and for arbitrary electromagnetic background. Our equations coincide with those of Frenkel in the approximation in which the latter have been obtained by Frenkel. Transition from approximate to exact equations yields two structural modifications of the theory. First, Frenkel condition on spin-tensor turns into the Pirani condition. Second, canonical momentum is no more proportional to velocity. Due to this, even when $μ=1$ (Frenkel case), the complete and approximate equations predict different behavior of particle. The difference between momentum and velocity means extra contribution into spin-orbit interaction. To estimate the contribution, we found exact solution to complete equations for the case of uniform magnetic field. While Frenkel electron moves around the circle, our particle experiences magnetic {\it Zitterbewegung}, that is oscillates in the direction of magnetic field with amplitude of order of Compton wavelength for the fast particle. Besides, the particle has dipole electric moment.

hep-th↗
arXiv2014

Frenkel electron and a spinning body in a curved background

We develop a variational formulation of a particle with spin in a curved space-time background. The model is based on a singular Lagrangian which provides equations of motion, a fixed value of spin and Frenkel condition on spin-tensor. Comparing our equations with those of Papapetrou we conclude that the Frenkel electron in a gravitational field has the same behavior as a rotating body in the pole-dipole and leading-spin approximation. Due to constraints presented in the formulation, position space is endowed with a noncommutative structure induced by the spin of the particle. Therefore, the model provides a physically interesting example of a noncommutative particle in a curved background.

hep-th↗
arXiv2014

Geometric Constructions Underlying Relativistic Description of Spin on the Base of Non-Grassmann Vector-Like Variable

Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with complicated structure of constraints. In this work we describe and discuss the spin fiber bundle which appeared in various mechanical models where spin is described by vector-like variable.

math-ph↗