Optical data processing using paraboloidal mirror segments

An optical data processing system using paraboloidal reflecting surfaces is disclosed. In the preferred embodiment the paraboloidal reflecting surfaces are segments of a paraboloidal mirror. A source of coherent light is in the focal plane of the first paraboloidal mirror segment which collimates the beam and reflects it toward a second paraboloidal mirror surface. The information to be analyzed, on a transparency for example, is placed in the collimated beam. The beam is reflected from the second paraboloidal mirror segment and focused on a Fourier transform plane. A photon detector could be placed in the Fourier transform plane or suitable spatial filters, with the filtered beam then being reflected from a third paraboloidal mirror segment to be focused on a reconstruction plane

Two dimensional general covariance from three dimensions

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of conserved charges that are associated with graphs in two dimensions and the Poisson algebra of the charges is closed. For 2-manifolds with boundary there are additional observables that have a Kac-Moody Poisson algebra. It is further shown that the theory is classically integrable and the general solution of the equations of motion is given. The quantum theory is described using Dirac quantization, and it is shown that there are quantum states associated with graphs in two dimensions.Comment: 10 pages (Latex), Alberta-Thy-19-9

Field and photon enhanced electron emission characteristics of cadmium sulphide field emitters

Field and photon enhanced electron emission characteristics of cadmium sulfide field emitter

Note on flat foliations of spherically symmetric spacetimes

It is known that spherically symmetric spacetimes admit flat spacelike foliations. We point out a simple method of seeing this result via the Hamiltonian constraints of general relativity. The method yields explicit formulas for the extrinsic curvatures of the slicings.Comment: 4 pages, to appear in PRD, reference added, typos correcte

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Constants of motion for vacuum general relativity

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the $SL(2,R)$ principal chiral model with certain `source' terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as explicit functionals on the phase space of Einstein gravity, and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D

General covariance, and supersymmetry without supersymmetry

An unusual four-dimensional generally covariant and supersymmetric SU(2) gauge theory is described. The theory has propagating degrees of freedom, and is invariant under a local (left-handed) chiral supersymmetry, which is half the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the theory reveals the remarkable feature that the local supersymmetry is a consequence of Yang-Mills symmetry, in a manner reminiscent of how general coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills symmetry. It is possible to write down an infinite number of conserved currents, which strongly suggests that the theory is classically integrable. A possible scheme for non-perturbative quantization is outlined. This utilizes ideas that have been developed and applied recently to the problem of quantizing gravity.Comment: 17 pages, RevTeX, two minor errors correcte

Stack-run adaptive wavelet image compression

We report on the development of an adaptive wavelet image coder based on stack-run representation of the quantized coefficients. The coder works by selecting an optimal wavelet packet basis for the given image and encoding the quantization indices for significant coefficients and zero runs between coefficients using a 4-ary arithmetic coder. Due to the fact that our coder exploits the redundancies present within individual subbands, its addressing complexity is much lower than that of the wavelet zerotree coding algorithms. Experimental results show coding gains of up to 1:4dB over the benchmark wavelet coding algorithm

Quantum Structure of Space Near a Black Hole Horizon

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one at each spatial point. The corresponding operator at each point is the product of the outgoing and ingoing null convergences, and describes the scale invariant quantum mechanics of a particle moving in an attractive $1/X^2$ potential. The variable $X$ that is analoguous to particle position is the square root of the conformal mode of the metric. We quantize the theory via Bohr quantization, which by construction turns the Hamiltonian constraint eigenvalue equation into a finite difference equation. The resulting spectrum gives rise to a discrete spatial topology exterior to the horizon. The spectrum approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur