Pauli approximation for a vector particle with anomalous magnetic moment in an external Coulomb field

Herein, a spin 1 particle with anomalous magnetic moment in an external Coulomb field is studied. We start with the relativistic tensor system of the Proca type in Cartesian coordinates. In these equations the Γ parameter is present related to an additional characteristic of the particle. In the case of an external magnetic field, it is interpreted as an anomalous magnetic moment. In the presence of an external electric field, additional interaction terms are presented as well; moreover, the terms of the first and second orders in parameter Γ appear. The case of an external Coulomb field is considered in detail. In the nonrelativistic approximation a Pauli type equation is obtained. In the nonrelativistic equation the separation of the variables with the use of spherical vectors is realized. One separate 2-nd order differential equation is found, in which additional interaction terms are missing. Besides, we derive systems of two coupled 2-nd order equations wherein linear and quadratic in parameter Γ interaction terms are presented. Previously, another approach was developed for analyzing the vector particle with anomalous magnetic moment. It was based on the use of tetrad formalism and separation of the variables in the Duffin – Kemmer equation with the help of the Wigner function. The nonrelativistic approximation was performed directly in the system of radial equations. Besides, previously formal Frobenius type solutions for an arising 4-th order differential equation were constructed; however, physically interpretable energy spectra were not found. We have proved that the radial equations derived by different methods are the same up to a simple liner transformation over two radial functions. In this paper, we have obtained a simpler 4-th order equation, the construction of Frobenius solutions becomes technically easier, but physical energy spectra are not found either.

Spin 3/2 particle: Puali – Fierz theory, non-relativistic approximation

The relativistic wave equation is well-known for a spin 3/2 particle proposed by W. E. Pauli and M. E. Fierz and based on the 16-component wave function with the transformation properties of the vector-bispinor. In this paper, we investigated the nonrelativistic approximation in this theory. Starting with the first-order equation formalism and representation of Pauli – Fierz equation in the Petras basis, also applying the method of generalized Kronecker symbols and elements of the complete matrix algebras, and decomposing the wave function into large and small nonrelativistic constituents with the help of projective operators, we have derived a Pauli-like equation for the 4-component wave function describing the non-relativistic particle with a 3/2 spin.

On the ‘Rigidity’ of the Force Field of a Moving Source

In the present paper, we propose a heuristic and intuitive approach to visualize how force fields “move” when their source moves at a constant velocity [Formula: see text] or accelerates with acceleration [Formula: see text] relative to a stationary observer. Our approach is based on the application of the principle of relativity and the principle of equivalence and holds regardless of the nature of the force field. The results presented here have been derived in the nonrelativistic approximation ([Formula: see text] and [Formula: see text], [Formula: see text] being the interval of time within which we observe the field). We shall show that in both cases of uniform and accelerated motion of the source, the field moves rigidly with the source. Namely, for every observer, however distant from the source, the field is always directed away from (or points towards) the present, instantaneous position of the source. We also show that these results are in agreement with what we know from experimental evidence and full-fledged physical theories (of electromagnetism and gravitation) beyond the nonrelativistic approximation. The proposed approach may be considered as a tool to facilitate students in graduate and undergraduate courses to familiarize themselves with (and self convince of) such a counter-intuitive feature of the force fields.

Квантовое трение и трение ван-дер-Ваальса в конфигурациях частица-пластина и пластина-пластина: нелокальные эффекты

Within the nonrelativistic approximation of fluctuation electrodynamics, using the specular reflection model and nonlocal permittivity of the metal, we have obtained simple analytical expressions for friction forces in particle – plate and plate – plate systems at relative motion of bodies at a constant velocity. It has been shown that at distances of about 1–10 nm for an Au nanoparticle (or gold plate) moving near another (identical) plate at rest, dissipative forces prove to be 2–4 orders of magnitude higher than when using the local Drude dielectric function.

Influences of the coordinate dependent noncommutative space on charged and spin currents

We study the charged and spin currents on a coordinate dependent noncommutative space. Starting from the noncommutative extended relativistic equation of motion, the nonrelativistic approximation is obtained by using the Foldy–Wouthuysen transformation, and then the charged and spin currents are derived by using the extended Drude model. We find that the charged current is twisted by modifying the off-diagonal elements of the Hall conductivity, however, the spin current is not affected up to leading order of the noncommutative parameter.

Quantum interference effects in conformal Weyl gravity

We investigate the effects of conformal gravity as a phase shift by quantum interference and alternate approach of Sagnac effect which is based on the anisotropy of the coordinate speed of light in the fourth-order theory of conformal Weyl space–time. In the nonrelativistic approximation, it has been shown that the phase shift of the interfering particle in neutron interferometer includes the potential terms with the Weyl parameter of the conformal fourth-order theory. Comparing the results of the measurement of the gravitational redshift by the interferometer in the gravitational field of the earth with our theoretical prediction, it has been obtained upper limit for the Weyl parameter as [Formula: see text].