Motion of electron with anomalous moments in parallel electric and magnetic fields

An accurate solution is obtained for the Dirac equation describing the motion of an electron with anomalous moments in constant, homogeneous, and parallel electric and magnetic fields. The system of solutions obtained is shown to be orthogonal and complete with respect to the scalar product defined in the null plane X^oX³=const. The solutions obtained pass smoothly in the limit to steadystate solutions describing the motion of an electron with anomalous moments in a homogeneous magnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 23–28, January, 1978.It remains to thank V. G. Bagrov for useful discussions of the work.     

Possible Astrophysical Effects of Gravitational Interaction of a Scalar Field Within the Framework of the Affine-Metric Theory of Gravitation

A gravitational interaction of a scalar field with conformal coupling \( n\frac{R}{6}{\upvarphi}^2 \) (n = const) is considered within the framework of the affine-metric theory of gravitation, with the interaction with torsion and nonmetricity taken into account. It is shown that for different values of the constant n different forms of nonlinearities are induced in the scalar field and, in particular, for n = –1 a nonlinearity corresponding to the potential of the axion field is induced. Possible astrophysical consequences of such an effect are considered.     

Thermoelastic vibrations of a semi-infinite strip

The forced vibrations of a thermoelastic strip (x₁ϵ [0, l], x₂ ⩾ 0) produced by a prescribed heating at the boundary x₂ = 0 are considered. The analysis is based on classical coupled thermoelastic theory (plane strain) and finite Fourier transforms. The solution of the problem under discussion is expressed in terms of the Lamé scalar and vector potentials.     

Gauged Nonlinear Sigma Model in the Instant Form: Hamiltonian and BRST Formulations

A gauged nonlinear sigma model in one space, one time dimension is considered in the usual instant form of dynamics on the hyperplanes x⁰ = const. The theory is seen to possess a local vector gauge symmetry. The Hamiltonian and BRST formulations of this theory are investigated with specific gauge choices.     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

The energy—momentum tensor, the trace identity and the Casimir effect

The trace identity associated with the scale transformation x^Μ → x′^Μ = e^-ρx^Μ on the Lagrangian density for the noninteracting electromagnetic field in the co-variant gauge is shown to be violated on a single plate on which the Dirichlet boundary conditionA ^Μ(t, x¹, x², x³ = -a) = 0 is imposed. It is however respected in free space, i.e. in the absence of the plate. These results reinforce our assertions in an earlier paper where the same exercise was carried out using the Lagrangian density for the free, massive, real scalar field in 2 + 1 dimensions.     

Electromagnetism in terms of its two degrees of freedom

Electromagnetism is described in terms of two scalar gauge-invariant variables. The role of gauge freedom in the quantization process when A^μ(x) is written in momentum space appears as the indetermination of a two-dimensional space-like plane orthogonal to the (null) momentum k^μ plus a c-number arbitrary function. Duality rotations can naturally be described as the freedom to choose two orthonormal vectors in the two-dimensional space-like plane. The action written in terms of the two dynamical degrees of freedom is explicitly invariant under finite duality rotations and the associated Noether current is gauge invariant. Finally, we establish the equivalence for the Poisson bracket relations (PBR's) (based on equal time and equal null-time PBR for the two degrees of freedom) between A^μ(x) and A^ν(x′) for any gauge.     

Flavour-changing effects on e+e-→Hbs̄,Hb̄s in the MSSM

Flavour-changing effects originating from the exchange of scalar particles in the processes e⁺e^-→H^xbs̄,H^xb̄s, with H^x≡h⁰,H⁰,A⁰, are investigated in the minimal supersymmetric standard model with non-minimal flavour violation at the one-loop level. The dominating SUSY-QCD contributions with squark–gluino loops are calculated and discussed. We consider the SUSY scenario with non-minimal flavour mixing in the down-type squark-mass matrix. The flavour-changing cross sections are derived, and we discuss the dependence on the MSSM parameters and the strength of flavour mixing. The values for the cross section can reach 10^-4 pb for the production of the heavy Higgs boson H⁰ or A⁰, and only 10^-7 pb for the light Higgs boson h⁰. Non-decoupling behaviour occurs for both h⁰,H⁰ production in the case of a common heavy SUSY mass scale.     

Global strings in extra dimensions: The full map of solutions,matter trapping,and the hierarchy problem

We consider (d ₀ + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d ₀ dimensions, endowed with a warp factor e ^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l _c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough distances l _c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane, where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems. The text was submitted by the authors in English.     

The trace identity and the planar Casimir effect

The familiar trace identity associated with the scale transformationx ^Μ → x′ ^Μ = e^-λ x ^Μ on the Lagrangian density for a noninteracting massive real scalar field in 2 + 1 dimensions is shown to be violated on a single plate on which the Dirichlet boundary condition Φ(t, x¹, x² = -a) = 0 is imposed. It is however respected in: (i) 1 + 1 dimensions in both free space and on a single plate on which the Dirichlet boundary condition Φ(t, x¹ = -a) = 0 holds and (ii) in 2 + 1 dimensions in free space, i.e. the unconstrained configuration. On the plate where Φ(t, x¹, x² = -a) = 0, the modified trace identity is shown to be anomalous with a numerical coefficient for the anomalous term equal to the canonical scale dimension, viz. 1/2. The technique of Bordaget al [Ann. Phys. (N.Y.),165, 162 (1985)] is used to incorporate the said boundary condition into the generating functional for the connected Green’s functions.     

Heavy-to-light correlators beyond the light cone

We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x ² = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x ² ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x ² = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%. The text was submitted by the authors in English.     

Dependence of the magnetic susceptibility of the palladium silver alloy system on temperature and composition

Starting from thermodynamic considerations an analytical expression (T, x) is given for the variation of the magnetic susceptibility of the substitutional Pd_1–x Ag _x alloy series with both temperatureT and fractional silver contentx. The observed rapid decrease of the isothermal susceptibility (T=const,x) with increasingx and the disappearance of the maximum of the low temperature isopleths (T,x=const) forx0.1 can be specified by three fitting constants related to microscopic model parameters.     

Possible signature of charged Higgs particles in high energy e+e− annihilation

Possible indications of the existence of charged Higgs scalar particles are discussed in an SU(2)×U(1) model. Four-K and six-K final states at high energy e⁺e^? annihilation are suggested for the signature of the existence of the charged scalar particle.     

Mössbauer spectroscopy and magnetic properties in thin films of FexNi100−x electroplated on silicon (1 0 0)

Fe_xNi_100−x thin films were produced by galvanostatic electrodeposition on Si (1 0 0), nominal thickness 2800 nm, and x ranging 7-20. The crystalline structure of the sample was determined by X-ray diffraction (XRD). The magnetic properties were investigated by vibration sample magnetometry (VSM) and room temperature ⁵⁷Fe Mössbauer spectroscopy. Conversion Electron Mössbauer spectroscopy (CEMS) in both film surfaces for the thick self-supported films showed that the magnetic moment direction is in the plane and conventional transmission (MS) that the directions are out of the plane films. The results were interpreted assuming a three-layer model where the external layer has in-plane magnetization and the internal one, out of plane magnetization.     

BRST quantization of a scalar particle in a curved background

The BRST formalism is employed to quantize a scalar particle and interactions with an external scalar field (x ) and vector gauge fieldA (x ) in the background of an arbitrary gravitational field. The second-quantized actions are obtained.     

非傍轴高斯光束传输特性的研究

基于非傍轴矢量光束横截面上光强的严格定义〈S_z〉,采用桶中功率定义光束的束宽、远场发散角以及M²因子. 以非傍轴矢量高斯光束为例,对光束的传输特性进行了详细的理论分析和数值计算,并与非傍轴标量理论的结果进行了比较分析. 研究表明,光源半宽ω₀/Λ<1时,传输特性的矢量描述与非傍轴标量描述有显著差别,随着ω₀/Λ的增大,两者趋于一致,并逐步过渡到 关键词： 非傍轴高斯光束 桶中功率 束宽 发散角     

Study of the structure and electrical properties of the copper nitride thin films deposited by pulsed laser deposition

Copper nitride thin films were prepared on glass and silicon substrates by ablating a copper target at different pressure of nitrogen. The films were characterized in situ by X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES) and ex situ by X-ray diffraction (XRD). The nitrogen content in the samples, x = [N]/[Cu], changed between 0 and 0.33 for a corresponding variation in nitrogen pressure of 9 × 10⁻² to 1.3 × 10⁻¹ Torr. Using this methodology, it is possible to achieve sub-, over- and stoichiometric films by controlling the nitrogen pressure. The XPS results show that is possible to obtain copper nitride with x = 0.33 (Cu₃N) and x = 0.25 (Cu₄N) when the nitrogen pressure is 1.3 × 10⁻¹ and 5 × 10⁻² Torr, respectively. The lattice constants obtained from XRD results for copper nitride with x = 0.25 is of 3.850 Å and with x = 0.33 have values between 3.810 and 3.830 Å. The electrical properties of the films were studied as a function of the lattice constant. These results show that the electrical resistivity increases when the lattice parameter is decreasing. The electrical resistivity of copper nitride with x = 0.25 was smaller than samples with x = 0.33.     

New proofs of the existence of the Feigenbaum functions

A new proof of the existence of analytic, unimodal solutions of the Cvitanovi-Feigenbaum functional equation g(x) = –g(g(–x)),g(x) 1 - const|x|^r at 0, valid for all in (0, 1), is given, and the existence of the Eckmann-Wittwer functions [8] is recovered. The method also provides the existence of solutions for certain given values ofr, and in particular, forr=2, a proof requiring no computer.