Analysis and measurement of electromagnetic scattering by pyramidal and wedge absorbers

By modifying the reflection coefficients in the Uniform Geometrical Theory of Diffraction a solution that approximates the scattering from a dielectric wedge is found. This solution agrees closely with the exact solution of Rawlins which is only valid for a few minor cases. This modification is then applied to the corner diffraction coefficient and combined with an equivalent current and geometrical optics solutions to model scattering from pyramid and wedge absorbers. Measured results from 12 inch pyramid absorbers from 2 to 18 GHz are compared to calculations assuming the returns add incoherently and assuming the returns add coherently. The measured results tend to be between the two curves. Measured results from the 8 inch wedge absorber are also compared to calculations with the return being dominated by the wedge diffraction. The procedures for measuring and specifying absorber performance are discussed and calibration equations are derived to calculate a reflection coefficient or a reflectivity using a reference sphere. Shaping changes to the present absorber designs are introduced to improve performance based on both high and low frequency analysis. Some prototypes were built and tested

Quantum Effective Action in Spacetimes with Branes and Boundaries

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions in the bulk factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane -- the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest order surface terms in the case of Robin and oblique boundary conditions. We briefly discuss multi-loop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.Comment: LaTeX, 25 pages, final version, to appear in Phys. Rev.

An introduction to quantum gravity

After an overview of the physical motivations for studying quantum gravity, we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader is therefore introduced, in a pedagogical way, to the functional integral quantization of gravitation and Yang-Mills theory. It is hoped that such a paper will remain useful for all lecturers or Ph.D. students who face the task of introducing (resp. learning) some basic concepts in quantum gravity in a relatively short time. In the second part, we outline selected topics such as the braneworld picture with the same covariant formalism of the first part, and spectral asymptotics of Euclidean quantum gravity with diffeomorphism-invariant boundary conditions. The latter might have implications for singularity avoidance in quantum cosmology.Comment: 68 pages, Latex file. Sections from 2 to 17 are published thanks to kind permission of Springe

Fedosov supermanifolds: II. Normal coordinates

The study of recently introduced Fedosov supermanifolds is continued. Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied.Comment: 12 pages, Late

TeV Scale Lee-Wick Fields out of Large Extra Dimensional Gravity

We study the gravitational corrections to the Maxwell, Dirac and Klein-Gorden theories in the large extra dimension model in which the gravitons propagate in the (4+n)-dimensional bulk, while the gauge and matter fields are confined to the four-dimensional world. The corrections to the two-point Green's functions of the gauge and matter fields from the exchanges of virtual Kaluza-Klein gravitons are calculated in the gauge independent background field method. In the framework of effective field theory, we show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a TeV scale Lee-Wick partner of every gauge and matter field as extra degrees of freedom in the theory. Thus the large extra dimension model of gravity provides a natural mechanism to the emergence of these exotic particles which were recently used to construct an extension of the Standard Model.Comment: 17 pages, 3 figures, references added, to appear in Phys. Rev.

Hydrogen-Helium Mixtures in the Interiors of Giant Planets

Equilibrium properties of hydrogen-helium mixtures under conditions similar to the interior of giant gas planets are studied by means of first principle density functional molecular dynamics simulations. We investigate the molecular and atomic fluid phase of hydrogen with and without the presence of helium for densities between $\rho=0.19$ g$$cm$^{-3}$ and $\rho=0.66$ g$$cm$^{-3}$ and temperatures from $T=500$K to $T=8000 {K}$. Helium has a crucial influence on the ionic and electronic structure of the liquid. Hydrogen molecule bonds are shortened as well as strengthened which leads to more stable hydrogen molecules compared to pure hydrogen for the same thermodynamic conditions. The {\it ab initio} treatment of the mixture enables us to investigate the validity of the widely used linear mixing approximation. We find deviations of up to 8% in energy and volume from linear mixing at constant pressure in the region of molecular dissociation.Comment: 13 pages, 18 figures, submitted to PR

Nonlinear couplings and tree amplitudes in gauge theories

Following a remark advanced by Feynman,we study the connection between the form of the nonlinear vertices involving gauge particles and the Abelian gauge invariance of physical tree amplitudes. We show that this requirement, together with some natural assumptions, fixes uniquely the structure of the Yang-Mills theory. However, the constraints imposed by the above property are not sufficient to single out the gauge theory of gravitation.Comment: 12 pages. Requires macros RevTeX, prepictex, pictex, postpictex. TeX source is 69373 byte

A pedagogical introduction to the Slavnov formulation of quantum Yang-Mills theory

Over the last few years, Slavnov has proposed a formulation of quantum Yang-Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.Comment: 16 pages, review pape

Vacuum Fluctuations of Energy Density can lead to the observed Cosmological Constant

The energy density associated with Planck length is $\rho_{uv}\propto L_P^{-4}$ while the energy density associated with the Hubble length is $\rho_{ir}\propto L_H^{-4}$ where $L_H=1/H$. The observed value of the dark energy density is quite different from {\it either} of these and is close to the geometric mean of the two: $\rho_{vac}\simeq \sqrt{\rho_{uv} \rho_{ir}}$. It is argued that classical gravity is actually a probe of the vacuum {\it fluctuations} of energy density, rather than the energy density itself. While the globally defined ground state, being an eigenstate of Hamiltonian, will not have any fluctuations, the ground state energy in the finite region of space bounded by the cosmic horizon will exhibit fluctuations $\Delta\rho_{\rm vac}(L_P, L_H)$. When used as a source of gravity, this $\Delta \rho$ should lead to a spacetime with a horizon size $L_H$. This bootstrapping condition leads naturally to an effective dark energy density $\Delta\rho\propto (L_{uv}L_H)^{-2}\propto H^2/G$ which is precisely the observed value. The model requires, either (i) a stochastic fluctuations of vacuum energy which is correlated over about a Hubble time or (ii) a semi- anthropic interpretation. The implications are discussed.Comment: r pages; revtex; comments welcom

HDO And SO2 Thermal Mapping On Venus II. The So2 Spatial Distribution Above And Within The Clouds

Sulfur dioxide and water vapor, two key species of Venus photochemistry, are known to exhibit significant spatial and temporal variations above the cloud top. In particular, ground-based thermal imaging spectroscopy at high spectral resolution, achieved on Venus in January 2012, has shown evidence for strong SO2 variations on timescales shorter than a day. We have continued our observing campaign using the TEXES high-resolution imaging spectrometer at the NASA InfraRed Telescope Facility to map sulfur dioxide over the disk of Venus at two different wavelengths, 7 mu m (already used in the previous study) and 19 mu m. The 7 mu m radiation probes the top of the H2SO4 cloud, while the 19 mu m radiation probes a few kilometers below within the cloud. Observations took place on October 4 and 5, 2012. Both HDO and SO2 lines are identified in our 7-mu m spectra and SO2 is also easily identified at 19 mu m. The CO2 lines at 7 and 19 mu m are used to infer the thermal structure. An isothermal/inversion layer is present at high latitudes (above 60 N and S) in the polar collars, which was not detected in October 2012. The enhancement of the polar collar in October 2012 is probably due to the fact that the morning terminator is observed, while the January data probed the evening terminator. As observed in our previous run, the HDO map is relatively uniform over the disk of Venus, with a mean mixing ratio of about 1 ppm. In contrast, the SO2 maps at 19 mu m show intensity variations by a factor of about 2 over the disk within the cloud, less patchy than observed at the cloud top at 7 mu m. In addition, the SO2 maps seem to indicate significant temporal changes within an hour. There is evidence for a cutoff in the SO2 vertical distribution above the cloud top, also previously observed by SPICAV/SOIR aboard Venus Express and predicted by photochemical models.NASA NNX-08AE38AIRTF AST-0607312, AST-0708074Astronom