Searcharxiv⌕ Search

arXiv subjects

Alexander J. Silenko

Publications and source records attributed to Alexander J. Silenko.

At least 73 records · Page 4Linked to original sources
arXiv2013

Spin in an arbitrary gravitational field

We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyse the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.

gr-qc↗
arXiv2013

Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods

Relativistic methods for the Foldy-Wouthuysen transformation of the ``step-by-step'' type already at the first step give an expression for the Hamilton operator not coinciding with the exact result determined by the Eriksen method. The methods agree for the zeroth and first orders in the Planck constant terms but do not agree for the second and higher-order terms. We analyze the benefits and drawbacks of various methods and establish their applicability boundaries.

math-ph↗
arXiv2013

Connection between beam polarization and systematical errors in storage ring electric-dipole-moment experiments

Analysis of spin dynamics in storage ring electric-dipole-moment (EDM) experiments ascertains that the use of initial vertical beam polarization allows to cancel spin-dependent systematical errors imitating the EDM effect. While the use of this polarization meets certain difficulties, it should be considered as an alternative or supplementary possibility of fulfilling the EDM experiment.

hep-ex↗
arXiv2013

Scalar particle in general inertial and gravitational fields and conformal invariance revisited

The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen representation. Similarity of manifestations of conformal invariance for massless scalar and Dirac particles is proved. New exact Foldy-Wouthuysen Hamiltonians are derived for both massive and massless scalar particles in a general static spacetime and in a frame rotating in the Kerr field approximated by a spatially isotropic metric. The latter case covers an observer on the ground of the Earth or on a satellite and takes into account the Lense-Thirring effect. High-precision formulas are obtained for an arbitrary spacetime metric. General quantum-mechanical equations of motion are derived. Their classical limit coincides with corresponding classical equations.

math-ph↗
arXiv2013

Quantum-mechanical description of spin-1 particles with electric dipole moments

The Proca-Corben-Schwinger equations for a spin-1 particle with an anomalous magnetic moment are added by a term describing an electric dipole moment, then they are reduced to a Hamiltonian form, and finally they are brought to the Foldy-Wouthuysen representation. Relativistic equations of motion are derived. The needed agreement between quantum-mechanical and classical relativistic equations of motion is proved. The scalar and tensor electric and magnetic polarizabilities of pointlike spin-1 particles (W bosons) are calculated for the first time.

hep-ph↗
arXiv2013

Validation of the Eriksen Method of the Exact Foldy-Wouthuysen Representation

The Eriksen method is proven to yield a correct and exact result when a sufficient condition of exact transformation to the Foldy-Wouthuysen (FW) representation is satisfied. Therefore, the Eriksen method is confirmed as valid. This makes it possible to establish the limits within which the approximate "step-by-step" methods are applicable. The latter is done by comparing the relativistic formulas for a Hamiltonian operator in the FW representation (obtained using those methods) and the known expression for the first terms of a series, which defines the expansion of this operator in powers of v/c as found by applying the Eriksen method.

math-ph↗
arXiv2011

Dirac fermions in strong gravitational fields

We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially isotropic metric. The quantum operator equations of motion are obtained and the semiclassical limit is analyzed. The comparison of the quantum mechanical and classical equations shows their complete agreement. The helicity dynamics in strong fields is discussed. Squaring the covariant Dirac equation explicitly shows a similarity of the interactions of electromagnetic and gravitational fields with a charged and spinning particle.

hep-th↗
arXiv2010

Potential for measurement of the tensor electric and magnetic polarizabilities of the deuteron in storage-ring experiments with polarized beams

Measurement of the tensor electric and magnetic polarizabilities of the deuteron is of great interest, especially in connection with the possibilities of COSY and GSI. These polarizabilities can be measured in storage rings by the frozen spin method providing a disappearance of g-2 precession. This method will be used in the planned deuteron electric-dipole-moment experiment in storage rings. The tensor electric polarizability of the deuteron significantly influences the buildup of the vertical polarization in the above experiment. The spin interactions depending on the electric dipole moment, the tensor electric polarizability, and main systematical errors caused by field misalignments have very different symmetries. For the considered experimental conditions, the sensitivity to the deuteron EDM of $1\times10^{-29} e\cdot$cm corresponds to measuring the both of tensor polarizabilities with an accuracy of $δα_T\approxδβ_T\approx5\times10^{-42}$ cm$^3$. This conservative estimate can be improved by excluding the systematical error caused by the field instability which is negligible for the measurement of the tensor polarizabilities. To find the tensor magnetic polarizability, the horizontal components of the polarization vector should be measured.

nucl-ex↗
arXiv2010

Potential for a new muon g-2 experiment

A new experiment to measure the muon g-2 factor is proposed. We suppose the sensitivity of this experiment to be about 0.03 ppm. The developed experiment can be performed on an ordinary storage ring with a noncontinuous field created by usual magnets. When the total length of straight sections of the ring is appropriate, the spin rotation frequency becomes almost independent of the particle momentum. In this case, a high-precision measurement of an average magnetic field can be carried out with polarized proton beams. A muon beam energy can be arbitrary. Possibilities to avoid a betatron resonance are analyzed and corrections to the g-2 frequency are considered.

hep-ex↗
arXiv2009

Foldy-Wouthuysen Transformation and Semiclassical Transition for Relativistic Quantum Mechanics

It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between quantum and classical theories is proved. The coincidence of the semiclassical equations of motion of particles and their spins with the corresponding classical equations is established. The Niels Bohr's correspondence principle is valid not only in the limit of large spin quantum numbers but also for particles with any spin as well as for spinless particles.

hep-th↗
arXiv2009

Spin dynamics in gravitational fields of rotating bodies and the equivalence principle

We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the precession of the classical spin is in a perfect agreement with the motion of the quantum spin derived from the Foldy-Wouthuysen approach for the Dirac particle in a curved spacetime. We show that the precession effect depends crucially on the choice of a tetrad. The results obtained are compared to the earlier computations for different tetrad gauges.

gr-qc↗
arXiv2008

Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field

We successively apply the generalized Case-Foldy-Feshbach-Villars (CFFV) and the Foldy-Wouthuysen (FW) transformation to derive the Hamiltonian for relativistic scalar particles in an electromagnetic field. In contrast to the original transformation, the generalized CFFV transformation contains an arbitrary parameter and can be performed for massless particles, which allows solving the problem of massless particles in an electromagnetic field. We show that the form of the Hamiltonian in the FW representation is independent of the arbitrarily chosen parameter. Compared with the classical Hamiltonian for point particles, this Hamiltonian contains quantum terms characterizing the quadrupole coupling of moving particles to the electric field and the electric and mixed polarizabilities. We obtain the quantum mechanical and semiclassical equations of motion of massive and massless particles in an electromagnetic field.

math-ph↗
arXiv2008

Classical and Quantum Spins in Curved Spacetimes

A comparative analysis of the Mathisson-Papapetrou and Pomeransky-Khriplovich equations is presented. Motion of spinning particles and their spins in gravitational fields and noninertial frames is considered. The angular velocity of spin precession defined by the Pomeransky-Khriplovich equations depends on the choice of the tetrad. The connection of such a dependence with the Thomas precession is established. General properties of spin interactions with gravitational fields are discussed. It is shown that dynamics of classical and quantum spins in curved spacetimes is identical. A manifestation of the equivalence principle in an evolution of the helicity is analyzed.

gr-qc↗
arXiv2008

Potential for measurement of the tensor magnetic polarizability of the deuteron in storage ring experiments

General formulas describing deuteron spin dynamics in storage rings with allowance for the tensor electric and magnetic polarizabilities are derived. It is found that an initially tensor-polarized deuteron beam can acquire a final horizontal vector polarization of the order of 1%. This effect allows one to measure the tensor magnetic polarizability of the deuteron in storage ring experiments. We also confirm an existence of the effect found by Baryshevsky and Gurinovich, hep-ph/0506135 and Baryshevsky, hep-ph/0510158; hep-ph/0603191 that the tensor magnetic polarizability of the deuteron causes the spin rotation with two frequencies and experiences beating for polarized deuteron beams in storage rings.

nucl-th↗
arXiv2007

Measuring the Tensor Polarization of Positronium

A method for measuring the tensor polarization in a positronium (Ps) beam is proposed, which is based on the determination of the Ps lifetime as a function of the orientation of a homogeneous magnetic field. The dependence of the orthopositronum (o-Ps) lifetime on the angle between the directions of the magnetic field and the tensor polarization of the Ps beam can be determined from the results of measurements from two or more field orientations.

cond-mat.mtrl-sci↗
arXiv2007

Effect of Electric and Magnetic Fields on Spin Dynamics in the Resonant Electric Dipole Moment Experiment

A buildup of the vertical polarization in the resonant electric dipole moment (EDM) experiment [Y. F. Orlov, W. M. Morse, and Y. K. Semertzidis, Phys. Rev. Lett. 96, 214802 (2006)] is affected by a horizontal electric field in the particle rest frame oscillating at a resonant frequency. This field is defined by the Lorentz transformation of an oscillating longitudinal electric field and a uniform vertical magnetic one. The effect of a longitudinal electric field is significant, while the contribution from a magnetic field caused by forced coherent longitudinal oscillations of particles is dominant. The effect of electric field on the spin dynamics was not taken into account in previous calculations. This effect is considerable and leads to decreasing the EDM effect for the deuteron and increasing it for the proton. The formula for resonance strengths in the EDM experiment has been derived. The spin dynamics has been calculated.

hep-ph↗