The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type I×fNI\times_{f} N

In this work we study the spectral zeta function associated with the Laplace operator acting on scalar functions defined on a warped product of manifolds of the type $I\times_{f} N$ where $I$ is an interval of the real line and $N$ is a compact, $d$-dimensional Riemannian manifold either with or without boundary. Starting from an integral representation of the spectral zeta function, we find its analytic continuation by exploiting the WKB asymptotic expansion of the eigenfunctions of the Laplace operator on $M$ for which a detailed analysis is presented. We apply the obtained results to the explicit computation of the zeta regularized functional determinant and the coefficients of the heat kernel asymptotic expansion.Comment: 29 pages, LaTe

Scalar Casimir effect between two concentric D-dimensional spheres

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel-Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between D-1 dimensional surfaces close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force. PACS number(s): 03.70.+k, 11.10.Kk, 11.10.Gh, 03.65.GeComment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1207.418

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding one-loop divergences and one-loop effective action actually exists. The present paper shows that, on the Euclidean four-ball, only the scalar part of perturbative modes for quantum gravity are affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is confined to the remaining fourth sector. The integral representation of the resulting zeta-function asymptotics is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.Comment: 25 pages, Revtex-4. Misprints in Eqs. (5.11), (5.14), (5.16) have been correcte

New Developments in the Spectral Asymptotics of Quantum Gravity

A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory. All of this is made possible by a peculiar spectral cancellation on the Euclidean 4-ball, here derived and discussed.Comment: 7 pages, latex file. Paper prepared for the Conference "QFEXT05: Quantum Field Theory Under the Influence of External Conditions", Barcelona, September 5 - September 9, 2005. In the final version, the presentation has been further improved, and yet other References have been adde

Recent NA48/2 and NA62 results

The NA48/2 Collaboration at CERN has accumulated and analysed unprecedented statistics of rare kaon decays in the $K_{e4}$ modes: $K_{e4}(+-)$ ($K^\pm \to \pi^+ \pi^- e^\pm \nu$) and $K_{e4}(00)$ ($K^\pm \to \pi^0 \pi^0 e^\pm \nu$) with nearly one percent background contamination. It leads to the improved measurement of branching fractions and detailed form factor studies. New final results from the analysis of 381 $K^\pm \to \pi^\pm \gamma \gamma$ rare decay candidates collected by the NA48/2 and NA62 experiments at CERN are presented. The results include a decay rate measurement and fits to Chiral Perturbation Theory (ChPT) description.Comment: Prepared for the Proceedings of "Moriond QCD and High Energy Interactions. March 22-29 2014." conferenc

Prospects for K+→π+ννˉK^+ \to \pi^+ \nu \bar{ \nu } at CERN in NA62

The NA62 experiment will begin taking data in 2015. Its primary purpose is a 10% measurement of the branching ratio of the ultrarare kaon decay $K^+ \to \pi^+ \nu \bar{ \nu }$, using the decay in flight of kaons in an unseparated beam with momentum 75 GeV/c.The detector and analysis technique are described here.Comment: 8 pages for proceedings of 50 Years of CP

Status of the apeNEXT project

We present the current status of the apeNEXT project. Aim of this project is the development of the next generation of APE machines which will provide multi-teraflop computing power. Like previous machines, apeNEXT is based on a custom designed processor, which is specifically optimized for simulating QCD. We discuss the machine design, report on benchmarks, and give an overview on the status of the software development

ChPT tests at the NA48 and NA62 experiments at CERN

The NA48/2 Collaboration at CERN has accumulated unprecedented statistics of rare kaon decays in the Ke4 modes: Ke4(+-) ($K^\pm \to \pi^+ \pi^- e^\pm \nu$) and Ke4(00) ($K^\pm \to \pi^0 \pi^0 e^\pm \nu$) with nearly one percent background contamination. The detailed study of form factors and branching rates, based on these data, has been completed recently. The results brings new inputs to low energy strong interactions description and tests of Chiral Perturbation Theory (ChPT) and lattice QCD calculations. In particular, new data support the ChPT prediction for a cusp in the $\pi^0\pi^0$ invariant mass spectrum at the two charged pions threshold for Ke4(00) decay. New final results from an analysis of about 400 $K^\pm \to \pi^\pm \gamma \gamma$ rare decay candidates collected by the NA48/2 and NA62 experiments at CERN during low intensity runs with minimum bias trigger configurations are presented. The results include a model-independent decay rate measurement and fits to ChPT description.Comment: XIIth International Conference on Heavy Quarks and Leptons 2014, Mainz, German

apeNEXT: A Multi-Tflops LQCD Computing Project

This paper is a slightly modified and reduced version of the proposal of the {\bf apeNEXT} project, which was submitted to DESY and INFN in spring 2000. .It presents the basic motivations and ideas of a next generation lattice QCD (LQCD) computing project, whose goal is the construction and operation of several large scale Multi-TFlops LQCD engines, providing an integrated peak performance of tens of TFlops, and a sustained (double precision) performance on key LQCD kernels of about 50% of peak speed