The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find interference effects between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar field=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing mass without mass and charge without charge. We examine its properties and a physical interpretation. We consider a linear version of the theory, finding the electromagnetic Lagrangian up to the second order of approximation with respect toh _v =g _v –n _v . We prove that in the zeroth and first orders of approximation there is no skewonoton interaction. We deal also with the Lagrangian for the scalar field (connected to the gravitational constant). We prove that in the zeroth and first orders of approximation the Lagrangian vanishes.     

Nonsymmetric Kaluza-Klein and Jordan-Thiry theory in a general non-Abelian case

This paper is devoted to an (n+4)-dimensional unification of NGT (nonsymmetric gravitation theory) and Yang-Mills theory in a Jordan-Thiry manner. We find interference effects between gravitational and Yang-Mills fields which appear to be due to the skew-symmetric part of the metric on the (n+4)-dimensional manifold (nonsymmetrically metrized principal fiber bundle). Our unification, called the nonsymmetric-non-Abelian Jordan-Thiry theory, becomes classical if the skew-symmetric part of the metric is zero. We find the Yang-Mills field Lagrangian up to the second order of approximation inh =g – . We also deal with the Lagrangian for the scalar field (connected to the gravitational constant). We consider the spin content of the theory and a relationship between the cosmological constant and the coupling constant between the skewon field and the gauge field in the first order of approximation. We show how to derive a dielectric model of a confinement from interference effects in these theories. We underline some similarities between the nonsymmetric Jordan-Thiry Lagrangian in the flat space limit and the soliton bag model Lagrangian.     

К ТЕОРИИ СПОНТАННОЙ Н АМАГНИЧЕННОСТИ ТОНКИХ СЛОЕВ. II. ЧАСТЬ)

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ПРИГОТОВЛЕНИЕ И ХАРА КТЕР ПОВЕРХНОСТИ ПЛАСТИНОК AgBr

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Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

Ferromagnetic resonance in thin cobalt films

The paper gives the results of measuring ferromagnetic resonance on thin cobalt films, vacuum deposited on unheated glass slides. The values of the (g-factor, the width of the curve, the effective stress and uniaxial induced anisotropy were determined as a function of the thickness of the film from measurements of the ferromagnetic absorption in a magnetic field normal and parallel to the surface of the film. Measurements were carried out on a frequency of 9200 MHz and on film thicknesses of 180 to 1800 Å. A qualitative explanation of the observed dependences is given.

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, . , , g-, , , . 9200 MHz 180–1800 Å. .

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The author thanks V. Kamberský and Z. Málek, C. Sc., for providing some of the cobalt films and for help in depositing and measuring the thicknesses, S. Kadeková and M. Polcarová for valuable advice in determining the structure of the films, J. Míová for carefully plotting the results of measurements and Z. Málek and O. tirand for carefully reading the paper and for valuable discussions.     

On the geometric structure underlying the eikonal equation

Given the eikonal equation _i=1 ³ (/x ⁱ ) ² =n ², we investigate the geometric structure that underlies the law of propagation of the wavefronts (x ¹,x ²,x ³) —ct=0. It turns out that Huygens' principle for the propagation of wavefronts is given in terms of a contact structure. Wavefronts are carried into wavefronts by contact transformations. As regards the wave-particle duality principle that arises in quantum mechanics, there is a natural geometric structure, a symplectic manifold (M ²ⁿ , ), which unifies Fermat's principle and the eikonal equation (Huygens' principle).On leave of absence from Institut für Angewandte Mathematik, Fachbereich Mathematik der Universität Mainz, Mainz, German Federal Republic.     

Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”

Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization |M|, susceptibility) and percolation cluster properties relating to the physical clusters, namely the Fortuin-Kasteleyn clusters (percolation probability P , percolation susceptibility _p, cluster size distributionn _l) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, P being identical to |M| in the thermodynamic limit, while finite-size corrections differ. In contrast, _p differs from even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to, but not to _p. NearT _c the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.     

The influence of the spectral asymmetry of X-ray emission lines on the results of studying defects in crystals by X-rays of different wavelength

Since the asymmetry of X-ray emission lines was found to influence the exact measurements of lattice parameters of powdered samples the author has revised the results she once obtained when carrying out exact measurements of the lattice parameter with radiations of various wavelengths for tungsten crystals containing admixtures of different elements. It is shown that with samples having an inhomogeneous distribution of the admixtures in the crystals the typical graphs of lattice parameter found originally remain when respecting the influence of the spectral asymmetry. On the other hand, with a sintered sample which has been homogeneized by long annealing the introduction of corrections to spectral asymmetry leads to an adjustment of the differences measured originally, for which it was difficult to find a probable explanation.

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On stress-energy tensors

We show how to introduce the Noether Operator of a (possibly constrained) variational principle even when the Lagrangian contains spinor fields (and their derivatives to any finite order). After relating that operator to the so-called canonical and symmetric stress-energy tensors, we construct explicitly the divergence by which these differ. A brief appendix illustrates the method of dealing with spinors by calculating T^v for the Dirac equation.     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.     

Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

Zum Problem der Exoelektronenemission

Zusammenfassung Es werden die zwei einfachsten Fälle der Exoelektronenemission untersucht und auf Grund dessen geeignete Verfahren zur Verarbeitung der Versuchsergebnisse vorgeschlagen.

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Inhomogeneity correlations in dirty superconductors,I

It is shown that fluctuations around the impurity averaged superconducting order parameter can be large due to interplay of disorder and (decoupled) interaction. Correlations () ² exceeding a critical value render superconductors with nonmagnetic impurities gapless. In addition to a mixed phase, 0 andM 0, a superconducting glass phase with =0 andM 0 is derived. In general, correlations () ² emerge from nonperturbative, saddle point solutions of a replicated matrix field theory. Replica symmetry, soft modes, and other order parameters are discussed.This work was supported by the Sonderforschungsbereich 123 of the Deutsche Forschungsgemeinschaft     

Types of von Neumann algebras associated with extremal invariant states

A globalized version of the following is proved. Let be a factor acting on a Hilbert space ,G a group of unitary operators on inducing automorphisms of ,x a vector separating and cyclic for which is up to a scalar multiple the unique vector invariant under the unitaries inG. Then either is of type III or _x is a trace of . The theorem is then applied to study the representations due to invariant factors state of asymptotically abelianC*-algebras, and to show that in quantum field theory certain regions in the Minkowski space give type III factors.     

Dependence of characteristics of hysteresis loops on dislocation densities for low-alloy Cr-Mo steel

The microstructure of specimens of low-alloy Cr-Mo steel subjected to various heat treatments and various plastic deformations is studied by transmission electron microscopy. The observations indicate that the decisive factors which control the coercive forceH _c, the initial permeability _i and the Rayleigh constant are the density and the arrangement of dislocations. The precipitates have only a secondary effect. The observed linear dependencesH _c ^1/2, _i ^–1/2, ^–1 ( —dislocation density) are in full agreement with the theoretical predictions.Dedicated to Academician Vladimír Hajko on the occasion of his 65th birthday.     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

A remark on a paper of J. F. Aarnes

LetA be aC*-algebra on the separable Hilbert space , and let be the von Neumann generated byA. LetG be a topological group anda(a) a representation ofG into the group of *-automorphisms ofA. Suppose that each (a) extends to a *-automorphism of , and suppose thata(a)(T)x, y is continuous for eachT inA andx, y and . Then, for a large class of groupsG, one has automatically thata(a)(T)x,y is continuous for allT in andx, y in .Supported in part by NSF Grant GP-9141.     

Calculation of the Tautomeric Properties of 3‐Formyl‐Tetrinic Acid by the ab initio and DFT Methods

We have carried out a nonempirical quantumchemical calculation with full optimization of the geometry of all theoretically possible tautomeric forms of 3formyltetrinic acid (FTRA) according to the Møller–Plesset secondorder perturbation theory with the use of a 6–31G(d) double zeta basis set. The correlation corrections to the total energy of molecules for optimized geometric configurations were calculated in the 631G(d,p) basis. All the possible tautomeric forms of FTRA and the harmonic vibrational frequencies were also calculated within the density functional theory (DFT) with the use of the Perdew–Burke–Ernzerhof (PBE) functional in a threeexponent basis. It is shown that FTRA in vapors (in the perfect gas approximation) exists in the form of a mixture of three enol forms, among which two exoforms predominate. The frequencies and forms of normal vibrations for each cisenol tautomer in the region of vibrations of ketogroups and double bonds differ widely, which permits identification of the tautomers present in the mixture. The possible mechanisms of enolenol transformations of 3acyltetrinic acids are discussed.     

Triton binding energy and three-nucleon potential

The method of continued fractions proposed by Horáek and Sasakawa is applied to calculate the binding energy of the triton. By this method, the Faddeev equation is solved very quickly. We solved it with 34 channels for the super-soft core (TRS), Paris (PARIS) and Argonne (AV) potentials with Tucson-Melbourne (TM) three-nucleon potential. The binding energy obtained from these realistic two-nucleon potentials without a threenucleon potential is at most 7.7 MeV. If we include the TM three-nucleon potential taking a cutoff mass of =800 MeV for the dipole NN form factor, the triton is overbound (9.3 9.7 MeV), whereas for =700 MeV, we get binding energies which almost agree with the experimental value; TRS+TM, 8.47; PARIS + TM, 8.32; AV+TM, 8.42 MeV.