Do You Have A Boyfriend Yet?

“Do you have a boyfriend yet?” That was the question that haunted me for most of my teenage years, the one I knew I would be asked at each family event and have to answer as nonchalantly as I could, “No, not yet,” without letting anyone know how embarrassed I felt. The feelings of anguish and anxiety continued in games of “Never Have I Ever,” going around the table with a group of less-than-close girlfriends sharing some of our first or best romantic experiences, so grateful that I had those one or two experiences that “kind of counted but maybe not so I really hope no one asks me to go into detail.” [excerpt

The Casimir Effect for Generalized Piston Geometries

In this paper we study the Casimir energy and force for generalized pistons constructed from warped product manifolds of the type $I\times_{f}N$ where $I=[a,b]$ is an interval of the real line and $N$ is a smooth compact Riemannian manifold either with or without boundary. The piston geometry is obtained by dividing the warped product manifold into two regions separated by the cross section positioned at $R\in(a,b)$. By exploiting zeta function regularization techniques we provide formulas for the Casimir energy and force involving the arbitrary warping function $f$ and base manifold $N$.Comment: 16 pages, LaTeX. To appear in the proceedings of the Conference on Quantum Field Theory Under the Influence of External Conditions (QFEXT11). Benasque, Spain, September 18-24, 201

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

Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension

In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a contour integral representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a $d$-dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly.Comment: 26 Pages, 1 Figur

Zeta Determinant for Laplace Operators on Riemann Caps

The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless $D-$dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.Comment: 19 pages, 1 figur

Noncommutative Einstein Equations

We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a diffeomorphisms and gauge invariant action constructed by using a matrix-valued scalar curvature. Interestingly the genuine noncommutative part of the dynamical equations is described only in terms of a particular tensor density that vanishes identically in the commutative limit. A noncommutative generalization of the energy-momentum tensor for the matter field is studied as well.Comment: 17 Pages, LaTeX, reference adde

Small Mass Expansion of Functional Determinants on the Generalized Cone

In this paper we compute the small mass expansion for the functional determinant of a scalar Laplacian defined on the bounded, generalized cone. In the framework of zeta function regularization, we obtain an expression for the functional determinant valid in any dimension for both Dirichlet and Robin boundary conditions in terms of the spectral zeta function of the base manifold. Moreover, as a particular case, we specify the base to be a $d$-dimensional sphere and present explicit results for $d=2,3,4,5$.Comment: LaTeX, 23 page

Results of the fifth international spectroradiometer comparison for improved solar spectral irradiance measurements and related impact on reference solar cell calibration

This paper reports on the results of the fifth spectral irradiance measurement intercomparison and the impact these results have on the spread of spectral mismatch calculations in the outdoor characterization of reference solar cell and photovoltaic (PV) devices. Ten laboratories and commercial partners with their own instruments were involved in the comparison. Solar spectral irradiance in clear sky condition was measured with both fast fixed and slow rotating grating spectroradiometers. This paper describes the intercomparison campaign, describes different statistical analysis used on acquired data, reports on the results, and analyzes the impact these results would have on the primary calibration of a c-Si PV reference cell under natural sunlight

Non-commutative Corrections in Spectral Matrix Gravity

We study a non-commutative deformation of general relativity based on spectral invariants of a partial differential operator acting on sections of a vector bundle over a smooth manifold. We compute the first non-commutative corrections to Einstein equations in the weak deformation limit and analyze the spectrum of the theory. Related topics are discussed as well.Comment: 32 Pages, LaTex. Some nonessential typos in intermediate calculations in sect. 3 and 4 are corrected. The final results are the sam