On the impossibility of using the longitude of the ascending node of GP-B for measuring the Lense–Thirring effect

The possibility of analyzing the node of the GP-B satellite in order to measure also the Lense–Thirring effect on its orbit is examined. This feature is induced by the general relativistic gravitomagnetic component of the Earth gravitational field. The GP-B mission has been launched in April 2004 and is aimed mainly to the measurement of the gravitomagnetic precession of four gyroscopes carried onboard at a claimed accuracy of 1%. of better. The aliasing effect of the solid Earth and ocean components of the solar K₁ tidal perturbations would make the measurement of the Lense–Thirring effect on the orbit unfeasible. Indeed, the science period of the GP-B mission amounts to almost one year. During this time span the Lense–Thirring shift on the GP-B node would be 164 milliarcseconds (mas), while the tidal perturbations on its node would have a period of the order of 10³ years and amplitudes of the order of 10⁵ mas.     

ФОТОЯДЕРНЫЙ ЭФФЕКТ Н А НИКЕЛЕ, МЕДИ И ЦИНКЕ

, - 17,6 , . , (8±4)·10^–23, (7±4)·10^–23 (4±2)·10^{–23 2}. , - .     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Dynamical structure of linearizedGL(4) gravities

The physical content of the three more natural models ofGL(4) gravity is analyzed, for the case of weak fields. The first model we deal with is the linearized version of Yang's onetensor-field gravity. It is shown that this is a scalar-tensor theory, with its scalar part contained in the symmetric tensorh , instead of appearing explicitly, externally to the symmetric tensorh , as happens in Brans-Dicke type of scalar-tensor theories. The second and the third linearized models, which can both be derived from the fourth-order action postulated by Yang, turn out to be two-tensor decoupled systems. In both cases one of the tensors is the symmetric weak metric gravity tensor field. The second tensor appearing in these two models, representing theGL(4)-gauge field, is either a linearized symmetric affinity (in the second model) or a linearized but nonsymmetric affinity (for the third model). It is shown that in these last two cases the affinity contains a helicity-3 propagating field. The connection is also given between the fourth-order system which determines the dynamical structure (for the last two models) of the metric tensor and the third-order Yang model of gravity. Owing to the presence of helicity-3 fields we show that it is better to regard Yang's action as an action for a two-tensor system instead of trying to recover from it a pure gravity (one-tensor-field) action. Finally, it is shown what is the dynamical structure of the second and third linearized two-tensor models which can be derived from Yang's action.On leave of absence from the Universidad Simón Bolívar.     

The one dimensional anderson model with off diagonal disorder: band centre anomaly

We study theE-dependence of the Lyapounov exponent <(E)> of an electron with energyE in the one dimensional Anderson model with off diagonal disorder. In the neighbourhood of the band centre we find for nonzero disorder E)>log^–1 E0 forE0, but all even moments of Re(E) diverge logarithmically. As the probability of Re (E)=0 decreases to zero forE0 we conclude that the electron is always exponentially localised.     

On Essential Incompleteness of Hertz’s Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertzs experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertzs experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertzs crucial experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtzs electrodynamics did not contradict any of Hertzs experimental observations of transverse components as Maxwells theory predicted. Moreover, as we now know from recently published Hertzs dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertzs experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtzs theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method.     

Higgs Field—Fermion Coupling in the Tensor Dirac Theory

In previous work, the Dirac and Einstein equations were unified in a tetradformulation of a Kaluza—Klein model which gives precisely the usualDirac—Einstein Lagrangian. In this model, the self-adjoint modes of the tetraddescribe gravity, whereas the isometric modes of the tetrad together with a scalarfield describe fermions. The tetrad Kaluza—Klein model is based on a constrainedYang—Mills formulation of the Dirac Lagrangian in which the bispinor field is mapped to a set of SL(2, R) × U(1) gauge potentialsA ^K _a and a complex scalarfield . In this paper we generalize the map (A ^K _a , ) to multiplets of nbispinor fields representing a fermion multiplet as in standard electroweak theory.We show that the Lagrangian for bispinor multiplets used in the Standard Modelbecomes a constrained Yang—Mills Lagrangian, for which the Higgs fielddetermines a noninvariant gauge metric, thereby breaking the full gauge symmetry.     

Plane-Symmetric Solitons of Spinor and Scalar Fields

We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor forms S= and P=i⁵; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant = _,^,, that becomes linear at 0. The spinor and the scalar fields in question interact with each other by means of a gravitational field which is given by a plane-symmetric metric. Exact plane-symmetric solutions to the gravitational, spinor and scalar field equations have been obtained. Role of gravitational field in the formation of the field configurations with limited total energy, spin and charge has been investigated. Influence of the change of the sign of energy density of the spinor and scalar fields on the properties of the configurations obtained has been examined. It has been established that under the change of the sign of the scalar field energy density the system in question can be realized physically iff the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. In general it has been shown that the choice of spinor field nonlinearity can lead to the elimination of scalar field contribution to the metric functions, but leaving its contribution to the total energy unaltered.     

Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions

Let ₁(x) and ₂(y) be two local fields in a conformal quantum field theory (CQFT) in two dimensional spacetime. It is then shown that the vector-valued distribution ₁(x)₂(y)|0 is a boundary value of a vectorvalued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that ₁(x)₂(y)|0 can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state |0. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two it its elements (a vacuum expansion is an operator product expansion applied to the vacuum).Work supported by Deutsche Forschungsgemeinschaft     

General relativity is a gauge type theory

It is shown that the Einstein-Maxwell theory of interacting electromagnetism and gravitation, can be derived from a first-order Lagrangian, depending on the electromagnetic field and on the curvature of a symmetric affine connection on the space-time M. The variation is taken with respect to the electromagnetic potential (a connection on a U(1) principal fiber bundle on M) and the gravitational potential (a connection on the GL(4, R) principal fiber bundle of frames on M). The metric tensor g does not appear in the Lagrangian, but it arises as a momentum canonically conjugated to . The Lagrangians of this type are calculated also for the Proca field, for a charged scalar field interacting with electromagnetism and gravitation, and for a few other interesting physical theories.     

The magnetic dipole moment of the 150 keV state of177Lu

The magnetic dipole interaction of the 150 keV state of¹⁷⁷Lu in an environment of metallic ytterbium has been investigated by time-differential perturbed angular correlation experiments. The measurements were performed in an external magnetic field of 0.4 T at room temperature. Two independent measurements at different - cascades give the same Larmor precession frequency. From the weighted average the magnetic dipole moment of the 150 keV state is derived as =+5.5(3) _K. From the angular correlation coefficient A₂₂=–0.042(7) of the (139–150) keV - cascade the mixing ratio =+0.21(4) is deduced. The coefficient A₂₂=+0.015(7) of the (1080–150) keV - cascade yields the mixing ratio =+0.08(4).     

Characterizations of the Kerr metric

For stationary, asymptotically flat solutions of Einstein's equations, covariant functionals of the metric variables are defined which characterize the Kerr metric uniquely. For instance, we obtain a generalization of the Bach tensor to stationary metrics, which vanishes if and only if the solution is Kerr. We also give a new interpretation of the Schwarzschild-to-Kerr-transformation. Our results might be applicable to simplify the proof of the uniqueness theorem for stationary black holes.     

On “Radiating Vaidya metric imbedded in deSitter space”

Mallett has generalized the Vaidya metric as well as the deSitter metric to obtain what he called the Vaidya-Schwarzschild-deSitter metric and has obtained the condition under which this metric represents a pure radiation field. The present note obtains the complete first integral of that equation as well as well as some particular solutions.     

A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.     

Levi–Civita effect in the polarizable vacuum (PV) representation of general relativity

The polarizable vacuum (PV) representation of general relativity (GR), derived from a model by Dicke and related to the TH formalism used in comparative studies of gravitational theories, provides for a compact derivation of the Levi–Civita effect (both magnetic and electric), herein demonstrated.This revised version was published online in April 2005. The publishing date was inserted.     

Specific heat of neutron-irradiated crystalline and of vapor-deposited amorphous silicon

We report on specific-heat measurements (0.1 K<T<2K) of heavily neutron-irradiated (4.8×10¹⁹ and 3×10²¹ n⁰/cm²) and as-received Si single crystals and of an evaporated amorphous Si film. The sample irradiated with the higher dose contains 6% amorphous regions, the other remains crystalline. The magnitude of the specific heat increases with amorphicity. However, already in the crystalline sample the specific heat exceeds the Debye contribution. We attribute the excess specific heat to exchange-coupled dangling bonds located at defects in crystalline environments and — for the amorphous sample — to dangling bonds in the amorphous network.Work supported by the Deutsche Forschungsgemeinschaft within the research program of Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Numerical Evidence for the Low-Mass Behavior of the One-Dimensional Rayleigh Gas with Local Interaction

Numerical investigations, supported by partial rigorous results suggest that the motion of a tagged particle of mass M on the line ¹ colliding with a free gas of particles of mass m in equilibrium is diffusive. It was conjectured that the diffusion constant D(M), for small mass M0, should approach D(m). (In dimension 1 this is a kind of continuity hypothesis.) Previous results of computer simulations are inconclusive. We report on some new computer results, which show clearly that there is no continuity, and the limit of D(M) as M0 is smaller than D(m). We compare with the corresponding results for a similar two-dimensional model, to which the continuity argument cannot be applied.     

Free Bosons and Tau-Functions for Compact Riemann Surfaces and Closed Smooth Jordan Curves. Current Correlation Functions

We study families of quantum field theories of free bosons on a compact Riemann surface of genus g. For the case g > 0, these theories are parameterized by holomorphic line bundles of degree g – 1, and for the case g = 0 — by smooth closed Jordan curves on the complex plane. In both cases we define a notion of -function as a partition function of the theory and evaluate it explicitly. For the case g > 0 the -function is an analytic torsion, and for the case g = 0, the regularized energy of a certain natural pseudo-measure on the interior domain of a closed curve. For these cases we rigorously prove the Ward identities for the current correlation functions and determine them explicitly. For the case g > 0, these functions coincide with those obtained by using bosonization. For the case g = 0, the -function we have defined coincides with the -function introduced as a dispersionless limit of the Sato's -function for the two-dimensional Toda hierarchy. As a corollary of the Ward identities, we note some recent results on relations between conformal maps of exterior domains and -functions. For this case, we also define a Hermitian metric on the space of all contours of given area. As another corollary of the Ward identities, we prove that the introduced metric is Kähler and the logarithm of the -function is its Kähler potential.     

Isotropic spherical coordinates

The method of using regularization to analyze singularities is applied to the Schwarzschild metric in isotropic spherical coordinates (3). It is found that there arises a singularity at the gravitational radius which does not satisfy the conditions of physical realizability (T =T ,T ₀ ⁰ =T =0). Consequently, this metric cannot be considered as corresponding to pure vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–87, April, 1987.     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln