N=2 topological gauge theory,the Euler characteristic of moduli spaces,and the Casson invariant

We discuss gauge theory with a topologicalN=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space and the partition function equals the Euler number () of . We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of connections. As a consequence of these considerations we propose the Euler number () of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. We also comment on the possibility of constructing a topological version of the Penner matrix model.From Oct. 1992: ictp, P.O. Box 586, I-34100 Trieste, Italy     

Interaction of running gratings of the space charge and conductivity in photorefractive Bi<Subscript>12</Subscript>Si(Ti)O<Subscript>20</Subscript> crystals

The simultaneous excitation and nonlinear interaction of the space-charge and photoconductivity gratings are studied experimentally in photorefractive Bi₁₂SiO₂₀ and Bi₁₂TiO₂₀. The measurements are performed using the diffraction technique, which implies the illumination of the crystal by an oscillating interference pattern (_r=532 nm) along with the application of dc and ac electric fields and detection of the diffracted probe beam (_p=650 nm). Such illumination excites the running photoconductivity grating, which interacts with the ac component of the applied field giving rise to the space-charge wave. Being the eigenmode of the space-charge oscillations, this wave reveals itself as a low-frequency resonant maximum at the frequency-transfer function of the detected signal. The drift mobilities of electrons are estimated using the developed technique: =(1.1–1.4)×10^-2 cm²/Vs (Bi₁₂SiO₂₀, T=296–298 K) and =2.8×10^-3 cm²/Vs (Bi₁₂TiO₂₀, T=293 K). PACS 42.65.Sf; 42.70.Nq     

Gravitational collapse with charge and small asymmetries I. Scalar perturbations

A recent analysis by Richard Price of spherical collapse with small nonspherical perturbations is here generalized to the case of an electrically charged collapsing star (0¦Q¦-M). The perturbations are confined to a scalar field generated by a nonspherical distribution of scalar charge in the star. As in the electrically neutral case, the scalar perturbations are probably a prototype for all others — electromagnetic, gravitational, and higherspin. The collapse is shown to produce a Reissner-Nordström black hole, and the scalar-field perturbations are shown to radiate completely away; but they die out more slowly the larger is the star's electric charge. For charge ¦Q¦M, the -pole part of the perturbation at fixedr and late times is dominated by a tail that dies out ast ^{–(2+ 2)}. But for ¦Q¦=M, the primary outgoing waves emitted from the star's surface are everywhere larger than the tail. At fixedr and late times they die as t^–(+2). Also, a calculation of the redshift shows that a collapsing star becomes black more slowly the larger is the star's electric charge.Supported in part by the National Science Foundation (GP-27304, GP-28027, GP-19887).     

Anticommutative Electric and Magnetic Charges, and the Monopole Question

The monopole question is treated anew in the light of a recent, strictly covariant,extended formulation of fermion quantum field theory naturally including alsoa pseudoscalar variety of conserved charges. The essential novelty lies in theresulting quantum property of anticommutivity between scalar and pseudoscalarcharge varieties, which should in particular apply to electric and magnetic charges.As an immediate outcome, there should no longer be any (Dirac-like) quantizationcondition relating these charges and binding the magnetic elementary charge tohave a very great strength. A generalized Lagrangian approach to the monopoleproblem is made truly viable, leading to two independent local gauge couplingswhich are separately generated by the electric and magnetic elementary chargesand are not allowed to interfere. This would prevent electric and magneticmonopoles from mutually interacting and would particularly account for theabsence of magnetic sources in ordinary electromagnetism. Within such aframework, an electric charge eigenstate with a nonzero eigenvalue is bound tohave a null magnetic charge expectation value, and the magnetic dipole momentof an electrically charged point fermion may actually be seen as resulting fromthe additional internal presence of a single magnetic charge subjected to a maximaluncertainty in sign. An easy estimate makes it allowable to assign to this chargea strength just equal to that of the partner electric charge. Such a conjecture leadsto a dual model of a charged point fermion where the electric and magneticroles can well be interchanged with no observable effects. In the associatedformalism, duality symmetry is already included without the need to appeal toany missing electromagnetic phenomenology to be discovered.     

A free-electron laser pumped by the soliton laser

We propose a scheme for building a free-electron laser in the soft X-ray region pumped by the soliton laser. Making use of soliton laser wave evolution shape and single-pass small signal analysis, we find that this laser has two special advantages over the previous electromagnetic wave undulator free-electron lasers. One is a very small mass-shift effect because of the special characteristics of soliton laser; the other is that it has an additional frequency tuning effect based on the conventional free-electron laser's tunability. We also obtain the small signal gain and present some discussion.     

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.     

Can particle creation by a black hole be described in terms of more familiar laboratory processes?

Particle creation by a black hole is described in terms of temperature corrections to the Casimir effect. The results of Levin, Polevoy, and Ritov for spectral and total Poynting vector for a fluctuating electromagnetic field in a plane vacuum gap between two arbitrary media with different temperatures in flat spacetime are applied to clarify the situation that exists between the horizon of a nonrotating black hole and spatial infinity. This helps to reveal the mechanism of particle creation. The Hawking radiation is born inside the bell formed by a potential barrier of a black hole in all the region [2M, ]. Its blackbody spectrum is due to the interaction of field fluctuations with the surface of the bell. The particles between the walls are virtual ones. They can become real after passing through the [3M, ] tail, appearing to an observer at future infinityJ ⁺ as real ones. The arguments for and against the present standpoint are discussed.     

Analysis of Propagation Conditions of ELF Radio Waves on the “Zeus”–Transbaikalia Path

We consider the results of measurements of the absolute values of horizontal electric and magnetic components of the electromagnetic field of the Zeus ELF radio facility at frequencies 33, 44, 82, and 188 Hz, carried out in Transbaikalia. Electromagnetic-field variations during 17 semidiurnal sessions (about 204 hours of synchronous records) are analyzed. The length of the Zeus–Transbaikalia path is approximately 4000 km.     

An Electromagnetic Trinity from “Negative Permittivity” and “Negative Permeability”

An electromagnetic trinity comprising vacuum, anti–vacuum, and nihility is postulated — after making use of materials with negative permittivity and negative permeability — to illuminate the structure of electromagnetic theory, at least insofar as the relationship of phase velocity with Poynting vector is concerned.     

Product states for local algebras

Let ()() and () () be the von Neumann algebras associated with the space-tiem regions and respectively in the vacuum representation of the free neutral massive scalar field. For suitably chosen spacelike separated regions and it is proved that there exists a normal product state of (), Some consequences for the algebraic structure of the local rings are pointed out.     

Propagation of electromagnetic waves in a random medium and nonzero rest mass of the photon

The propagation of electromagnetic waves is studied in a Maxwell vacuum with 0. The photon loses energy during its propagation through this vacuum. This dissipation of energy is related to the fluctuation of the refractive index of the underlying vacuum. There exists a bounded and unique solution in the limit 0 in the asymptotic region. The geometric structure of the background space-time is Finslerian in nature.     

Effect of the polarization of the electromagnetic wave on wave energy absorption caused by the linear transformation of waves

The paper deals with the experimental verification of the effect of the polarization of the electromagnetic wave on the linear transformation of waves in an inhomogeneous magnetoactive plasma. Experiments were carried out in magnetic field satisfying condition _ce/>1, where _ce, are the electron cyclotron frequency and the frequency of the electromagnetic wave. The expressive dependence of the electromagnetic wave energy absorption on its polarization found experimentally is in excellent agreement with the theory.The authors wish to thank the director of the Institute of Plasma Physics Dr. J. Váa for his interest in this work and to Drs. R. Klíma, V. Kopecký and J. atlov for many valuable discussions and comments.     

On the Formation of Centered Shock Waves in Gas Bubbles under the Conditions of Acoustic Cavitation

The possibility of the formation of centered shock waves in collapsing gas bubbles under the conditions of acoustic cavitation is considered. In this case, the overturning of the front of compression waves occurs at the instant the waves reach the center of the cavitation bubble, resulting in the highest possible temperatures and pressures inside the bubble. Examination of the magnetohydrodynamic equations has shown that the law of the motion of the wall of a bubble at the final stage of compression, described by the Rayleigh–Plesset equation, has a universal form and coincides with the condition of the formation of a spherically symmetric centered shock wave with the adiabatic constant = 5/3. For < 5/3, the collapse of a bubble occurs within a shorter time than it takes for a spherically symmetric centered shock wave to form. In this case, the overturning of the front of compression waves occurs earlier than they reach the center of the bubble, and shock waves are formed inside the bubble at different points. The most appropriate condition for the detection of centered shock waves is the cavitation in cryogenic fluids, such as helium, for which 5/3.     

On the strength of Einstein's unified field equations

Einstein's concept of the strength of a system of field equations, which has been related in a simple way to the amount of initial data required for the system, is examined for his last unified field theory. The apparently surprising weakness of this system is traced to the high order of the associated electromagnetic field equations. These equations allow the existence of purely electric longitudinal waves, in spite of the absence of any photon mass.     

The vacuum and lightcone quantization of interaction Hamiltonians

Let denote the conformally invariant neutral free scalar field on ×S ⁿ. The naive lightcone Hamiltonian for a ^p interaction is given by c^p, where C denotes a lightcone in ×S ⁿ, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n3 is odd, p>2, and p(n–1)0 mod 4.     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .     

Sensitivity of spinI=5/2 perturbed-angular-correlation measurements to combined magnetic-dipole and electric-quadrupole hyperfine interactions

To design, analyze, and interpret perturbed-angular-correlation (PAC) experiments, the theory of the combined nuclear-magnetic-dipole and nuclear-electric-quadrupole interaction is applied. The applications involve polycrystalline sources that contain spinI=5/2 intermediate-quantum-level PAC probes. Frequenciesw _kk , amplitudesa _kk , and perturbation functionsG ₂₂ (t) are calculated for various values of the combined-interaction parameters, , and, wheny=w _L /W _Q is fixed at 30. For relatively large values ofy, the weak shift in them-state energies caused by the electric-quadrupole interaction generally produces a large change in the resulting perturbation function, and the effect is sensitive to the specific values of the parameters, , and. This sensitivity arises because the weak shift inm-state energies produces heterodyning. Moreover, this analysis indicates that PAC measurements of combined interactions in highly-distorted crystals (W _Q 0 and0) can provide potentially more information than previously thought. This analysis strongly suggests that more experimental investigations should be performed on highly-distorted crystals.     

On purely radiative space-times

The existence of space-times representing pure gravitational radiation which comes in from infinity and interacts with itself is discussed. They are characterized as solutions of Einstein's vacuum field equations possessing a smooth structure at past null infinity which forms the future null cone at past timelike infinity with complete generators. The pure radiation problem is analysed where free initial data for Einstein's field equations are prescribed on the null cone at past time-like infinity. It is demonstrated how the pure radiation problem can be formulated as a local initial value problem for the symmetric hyperbolic system of reduced conformal vacuum field equations. Its solutions are uniquely determined by the free data.Work supported by a Heisenberg-fellowship of the Deutsche Forschungsgemeinschaft     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.