Gravitons in One-Loop Quantum Cosmology: Correspondence Between Covariant and Non-Covariant Formalisms

The discrepancy between the results of covariant and non-covariant one-loop calculations for higher-spin fields in quantum cosmology is analyzed. A detailed mode-by-mode study of perturbative quantum gravity about a flat Euclidean background bounded by two concentric 3-spheres, including non-physical degrees of freedom and ghost modes, leads to one-loop amplitudes in agreement with the covariant Schwinger-DeWitt method. This calculation provides the generalization of a previous analysis of fermionic fields and electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a well-defined 3+1 decomposition.Comment: 29 pages, latex, recently appearing in Physical Review D, volume 50, pages 6329-6337, November 1994. The authors apologize for the delay in circulating the paper, due to technical problems now fixe

Counter-propagating entangled photons from a waveguide with periodic nonlinearity

The conditions required for spontaneous parametric down-conversion in a waveguide with periodic nonlinearity in the presence of an unguided pump field are established. Control of the periodic nonlinearity and the physical properties of the waveguide permits the quasi-phase matching equations that describe counter-propagating guided signal and idler beams to be satisfied. We compare the tuning curves and spectral properties of such counter-propagating beams to those for co-propagating beams under typical experimental conditions. We find that the counter-propagating beams exhibit narrow bandwidth permitting the generation of quantum states that possess discrete-frequency entanglement. Such states may be useful for experiments in quantum optics and technologies that benefit from frequency entanglement.Comment: submitted to Phys. Rev.

Nothing as Not-Being : Some Literary Contexts that Bear on Plato and on Parmenides

In the main Section of this paper I examine a certain characterizing use of meden/ouden and medeis/oudeis in pre-Platonic non-philosophical contexts. The passages discussed and analyzed offer cle.ar and suggestive illustrations of the assimilation of nothing or nobody to not-being. In the concluding Section I explore connections between that use and philosophical concepts,with particular reference to Plato\u27s doctrine of degrees of reality. The dialectic of being in classical Greek speculation focuses not on \u27What there is\u27 but on \u27what it is\u27 or \u27how it is\u27; not on existence but on physis, constitution, or form

A Non-Singular One-Loop Wave Function of the Universe From a New Eigenvalue Asymptotics in Quantum Gravity

Recent work on Euclidean quantum gravity on the four-ball has proved regularity at the origin of the generalized zeta-function built from eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary conditions are imposed in the de Donder gauge. The hardest part of the analysis involves one of the four sectors for scalar-type perturbations, the eigenvalues of which are obtained by squaring up roots of a linear combination of Bessel functions of integer adjacent orders, with a coefficient of linear combination depending on the unknown roots. This paper obtains, first, approximate analytic formulae for such roots for all values of the order of Bessel functions. For this purpose, both the descending series for Bessel functions and their uniform asymptotic expansion at large order are used. The resulting generalized zeta-function is also built, and another check of regularity at the origin is obtained. For the first time in the literature on quantum gravity on manifolds with boundary, a vanishing one-loop wave function of the Universe is found in the limit of small three-geometry, which suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory.Comment: 21 Pages, Latex and .eps files with JHEP3 style. The discussion in Section 5 has been improved, and Ref. 26 has been adde

Mind\u27s Commitment to the Real: Parmenides B8.34ff

It is through an analysis of this passage that I can explain most clearly and directly a certain conception of the relation of mind to reality for which I also find evidence in other texts, in some of the characteristic aspects and themes of Parmenicles\u27 poem, and which I consider philosophically and historically important.

On Darboux-Treibich-Verdier potentials

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-\omega_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.Comment: 8 page

Earth and Stars in the Cosmology of Xenophanes

The doxography for Xenophanes of Colophon unambiguously attributes to him a theory that all the meteora, i.e. all \u27objects suspended above us\u27 or \u27objects seen in the sky\u27 are different types of clouds. My concern in this paper is with two sets of assumptions that are likely to have framed Xenophanes\u27 theory: a) assumptions concerning the size and shape of the eareth, and b) assumptions concerning the motions of the fixed stars

Determination of the Strong Coupling \boldmath{\as} from hadronic Event Shapes and NNLO QCD predictions using JADE Data

Event Shape Data from $e^+e^-$ annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV are used to determine the strong coupling $\alpha_S$. QCD predictions complete to next-to-next-to-leading order (NNLO), alternatively combined with resummed next-to-leading-log-approximation (NNLO+NLLA) calculations, are used. The combined value from six different event shape observables at the six JADE centre-of-mass energies using the NNLO calculations is $\alpha_S(M_Z)$= 0.1210 +/- 0.0007(stat.) +/- 0.0021(expt.) +/- 0.0044(had.) +/- 0.0036(theo.) and with the NNLO+NLLA calculations the combined value is $\alpha_S$= 0.1172 +/- 0.0006(stat.) +/- 0.0020(expt.) +/- 0.0035(had.) +/- 0.0030(theo.) . The stability of the NNLO and NNLO+NLLA results with respect to missing higher order contributions, studied by variations of the renormalisation scale, is improved compared to previous results obtained with NLO+NLLA or with NLO predictions only. The observed energy dependence of $\alpha_S$ agrees with the QCD prediction of asymptotic freedom and excludes absence of running with 99% confidence level.Comment: 9 pages, EPHJA style, 4 figures, corresponds to published version with JADE author lis

Transverse Spin at PHENIX: Results and Prospects

The Relativistic Heavy Ion Collider (RHIC), as the world's first and only polarized proton collider, offers a unique environment in which to study the spin structure of the proton. In order to study the proton's transverse spin structure, the PHENIX experiment at RHIC took data with transversely polarized beams in 2001-02 and 2005, and it has plans for further running with transverse polarization in 2006 and beyond. Results from early running as well as prospective measurements for the future will be discussed.Comment: 6 pages, 2 figures, presented at Transversity 2005, Como, Ital