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Alexander J. Silenko

Publications and source records attributed to Alexander J. Silenko.

At least 55 records · Page 3Linked to original sources
arXiv2016

Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle

The exact exponential Foldy-Wouthuysen transformation operator applicable for a particle with an arbitrary spin is derived. It can be successfully utilized for verifying any Foldy-Wouthuysen transformation method based on the exponential operator. When a verified method is relativistic, the relativistic exponential operator should be expanded in the semirelativistic power series. The use of the obtained exponential operator for a derivation of the Foldy-Wouthuysen Hamiltonian makes it possible to check the validity of any other method of the Foldy-Wouthuysen transformation, while this possibility may need a greater computational effort.

math-ph↗
arXiv2016

Manifestations of the rotation and gravity of the Earth in high-energy physics experiments

The inertial (due to rotation) and gravitational fields of the Earth affect the motion of an elementary particle and its spin dynamics. This influence is not negligible and should be taken into account in high-energy physics experiments. Earth's influence is manifest in perturbations in the particle motion, in an additional precession of the spin, and in a change of the constitutive tensor of the Maxwell electrodynamics. Bigger corrections are oscillatory, and their contributions average to zero. Other corrections due to the inhomogeneity of the inertial field are not oscillatory but they are very small and may be important only for the storage ring electric dipole moment experiments. Earth's gravity causes the Newton-like force, the reaction force provided by a focusing system, and additional torques acting on the spin. However, there are no observable indications of the electromagnetic effects due to Earth's gravity.

gr-qc↗
arXiv2016

Local Lorentz transformations and Thomas effect in general relativity

The tetrad method is used for an introduction of local Lorentz frames and a detailed analysis of local Lorentz transformations. A formulation of equations of motion in local Lorentz frames is based on the Pomeransky-Khriplovich gravitoelectromagnetic fields. These fields are calculated in the most important special cases and their local Lorentz transformations are determined. The local Lorentz transformations and the Pomeransky-Khriplovich gravitoelectromagnetic fields are applied for a rigorous derivation of a general equation for the Thomas effect in Riemannian spacetimes and for a consideration of Einstein's equivalence principle and the Mathisson force.

gr-qc↗
arXiv2016

General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method

General properties of the Foldy-Wouthuysen transformation which is widely used in quantum mechanics and quantum chemistry are considered. Merits and demerits of the original Foldy-Wouthuysen transformation method are analyzed. While this method does not satisfy the Eriksen condition of the Foldy-Wouthuysen transformation, it can be corrected with the use of the Baker-Campbell-Hausdorff formula. We show a possibility of such a correction and propose an appropriate algorithm of calculations. An applicability of the corrected Foldy-Wouthuysen method is restricted by the condition of convergence of a series of relativistic corrections.

math-ph↗
arXiv2015

Field of a moving locked charge as applied to beam-beam interactions in storage rings

It is shown that the Lorentz transformation cannot in general be formally applied to potentials and fields of particles locked in a certain region. In particular, this property relates to nucleons in nuclei and to particles and nuclei in storage rings. Even if they move with high velocities, their electric fields are defined by the Coulomb law. The result obtained is rather important for the planned deuteron electric-dipole-moment experiment in storage rings.

physics.acc-ph↗
arXiv2015

General dynamics of tensor polarization of particles and nuclei in external fields

The tensor polarization of particles and nuclei becomes constant in the coordinate system rotating with the same angular velocity as the spin and rotates in the lab frame with the above angular velocity. The general equation defining the time dependence of the tensor polarization is derived. An explicit form of dynamics of this polarization is found in the case when the initial polarization is axially symmetric.

hep-ph↗
arXiv2015

Spin precession of a particle with an electric dipole moment: contributions from classical electrodynamics and from the Thomas effect

The new derivation of the equation of the spin precession is given for a particle possessing electric and magnetic dipole moments. Contributions from classical electrodynamics and from the Thomas effect are explicitly separated. A fully covariant approach is used. The final equation is expressed in a very simple form in terms of the fields in the instantaneously accompanying frame. The Lorentz transformations of the electric and magnetic dipole moments and of the spin are derived from basic equations of classical electrodynamics. For this purpose, the Maxwell equations in matter are used and the result is confirmed by other methods. An antisymmetric four-tensor is correctly constructed from the electric and magnetic dipole moments.

hep-ph↗
arXiv2015

New symmetry properties of pointlike scalar and Dirac particles

New symmetry properties are found for pointlike scalar and Dirac particles (Higgs boson and all leptons) in Riemannian and Riemann-Cartan spacetimes in the presence of electromagnetic interactions. A Hermitian form of the Klein-Gordon equation for a pointlike scalar particle in an arbitrary n-dimensional Riemannian (or Riemann-Cartan) spacetime is obtained. New conformal symmetries of initial and Hermitian forms of this equation are ascertained. In the above spacetime, general Hamiltonians in the generalized Feshbach-Villars and Foldy-Wouthuysen representations are derived. The conformal-like transformation conserving these Hamiltonians is found. Corresponding conformal symmetries of a Dirac particle are determined. It is proven that all conformal symmetries remain unchanged by an inclusion of electromagnetic interactions.

hep-th↗
arXiv2015

General method of the relativistic Foldy-Wouthuysen transformation and proof of validity of the Foldy-Wouthuysen Hamiltonian

A general method of the Foldy-Wouthuysen transformation is developed. This method is applicable to relativistic particles with any spin in arbitrarily strong external fields. It can be used when the de Broglie wavelength is much smaller than the characteristic distance. Contrary to previously developed relativistic methods, the present method satisfies the condition of the exact Foldy-Wouthuysen transformation and is well substantiated. The derived relativistic Foldy-Wouthuysen Hamiltonian is expanded in powers of the Planck constant. In this expansion, terms proportional to the zero and first powers are determined exactly in accordance with the above condition and terms proportional to higher powers are not specified. The obtained result agrees with the corresponding formula for the Foldy-Wouthuysen Hamiltonian previously deduced by an iterative relativistic method and proves the validity of results obtained with this formula.

math-ph↗
arXiv2015

Spin-torsion coupling and gravitational moments of Dirac fermions: theory and experimental bounds

We discuss the quantum dynamics of the Dirac fermion particle in a gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational and the Lorentz gravitational moments. The anomalous gravitomagnetic and gravitoelectric moments are ruled out on the basis of the covariance arguments. We derive the general Foldy-Wouthuysen transformation for an arbitrary configuration of the gauge gravitational field without assuming it weak. Making use of the Foldy-Wouthuysen Hamiltonian for the Dirac particle coupled to magnetic field in a noninertial reference system, we analyze the recent experimental data and obtain bounds on the spacetime torsion.

hep-th↗
arXiv2015

Energy expectation values of a particle in nonstationary fields

We show that the origin of the nonequivalence of Hamiltonians in different representations is a change of the form of the time-derivative operator at a time-dependent unitary transformation. This nonequivalence does not lead to an ambiguity of the energy expectation values of a particle in nonstationary fields but assigns the basic representation. It has been explicitly or implicitly supposed in previous investigations that this representation is the Dirac one. We prove the alternative assertion about the basic role of the Foldy-Wouthuysen representation. We also derive the general equation for the energy expectation values in the Dirac representation. As an example, we consider a spin-1/2 particle with anomalous magnetic and electric dipole moments in strong time-dependent electromagnetic fields. We apply the obtained results to a spin-1/2 particle in a plane monochromatic electromagnetic wave and give an example of the exact Foldy-Wouthuysen transformation in the nonstationary case.

math-ph↗
arXiv2014

Comparison of Spin Dynamics in the Cylindrical and Frenet-Serret Coordinate Systems

A comparative analysis of a description of spin dynamics in the cylindrical and Frenet-Serret coordinate systems is carried out. An equivalence of these two systems is shown. A possibility of efficient use of the cylindrical coordinate system for a calculation of spin evolution of particles and nuclei in accelerators and storage rings is caused by an immobility of its coordinate axes relative to stationary detectors.

physics.acc-ph↗
arXiv2014

Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles

Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines the Coriolis-like and centrifugal-like accelerations and presents the quantum-mechanical description of the frame-dragging effect.

gr-qc↗
arXiv2014

High-precision description and new properties of a spin-1 particle in a magnetic field

The exact Foldy-Wouthuysen Hamiltonian is derived for a pointlike spin-1 particle with a normal magnetic moment in a nonuniform magnetic field. For a uniform magnetic field, it is exactly separated into terms linear and quadratic in spin. New unexpected properties of a particle with an anomalous magnetic moment are found. Spin projections of a particle moving in a uniform magnetic field are not integer and the tensor polarization is asymmetric in the plane orthogonal to the field. Previously described spin-tensor effects caused by the tensor magnetic polarizability exist not only for nuclei but also for pointlike particles.

quant-ph↗
arXiv2014

Spin effects and compactification

We consider the dynamics of Dirac particles moving in the curved spaces with one coordinate subjected to compactification and thus interpolating smoothly between three- and two-dimensional spaces. We use the model of compactification, which allows us to perform the exact Foldy-Wouthuysen transformation of the Dirac equation and then to obtain the exact solutions of the equations of motion for momentum and spin in the classical limit. The spin precesses with the variable angular velocity, and a "flick" may appear in the remnant two-dimensional space once or twice during the period. We note an irreversibility in the particle dynamics because the particle can always penetrate from the lower-dimensional region to the higher-dimensional region, but not inversely.

gr-qc↗
arXiv2013

Foldy-Wouthyusen Transformation and Semiclassical Limit for Relativistic Particles in Strong External Fields

A general method of the Foldy-Wouthyusen (FW) transformation for relativistic particles of arbitrary spin in strong external fields has been developed. The use of the found transformation operator is not restricted by any definite commutation relations between even and odd operators. The final FW Hamiltonian can be expanded into a power series in the Planck constant which characterizes the order of magnitude of quantum corrections. Exact expressions for low-order terms in the Planck constant can be derived. Finding these expressions allows to perform a simple transition to the semiclassical approximation which defines a classical limit of the relativistic quantum mechanics. As an example, interactions of spin-1/2 and scalar particles with a strong electromagnetic field have been considered. Quantum and semiclassical equations of motion of particles and their spins have been deduced. Full agreement between quantum and classical theories has been established.

math-ph↗