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

Low-Energy Effective Action in Non-Perturbative Electrodynamics in Curved Spacetime

We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection (that we call the electromagnetic field) is constant we compute the first two coefficients of the non-perturbative asymptotic expansion of the heat kernel which are of zero and the first order in Riemannian curvature and of arbitrary order in the electromagnetic field. We apply these results to the study of the effective action in non-perturbative electrodynamics in four dimensions and derive a generalization of the Schwinger's result for the creation of scalar and spinor particles in electromagnetic field induced by the gravitational field. We discover a new infrared divergence in the imaginary part of the effective action due to the gravitational corrections, which seems to be a new physical effect.Comment: LaTeX, 42 page

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

Kinematics in Matrix Gravity

We develop the kinematics in Matrix Gravity, which is a modified theory of gravity obtained by a non-commutative deformation of General Relativity. In this model the usual interpretation of gravity as Riemannian geometry is replaced by a new kind of geometry, which is equivalent to a collection of Finsler geometries with several Finsler metrics depending both on the position and on the velocity. As a result the Riemannian geodesic flow is replaced by a collection of Finsler flows. This naturally leads to a model in which a particle is described by several mass parameters. If these mass parameters are different then the equivalence principle is violated. In the non-relativistic limit this also leads to corrections to the Newton's gravitational potential. We find the first and second order corrections to the usual Riemannian geodesic flow and evaluate the anomalous nongeodesic acceleration in a particular case of static spherically symmetric background.Comment: 31 pages, no figures, discussion of Pioneer anomaly remove

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

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

Results from an ethnographically-informed study in the context of test driven development

Background: Test-driven development (TDD) is an iterative software development technique where unit tests are defined before production code. Previous studies fail to analyze the values, beliefs, and assumptions that inform and shape TDD. Aim: We designed and conducted a qualitative study to understand the values, beliefs, and assumptions of TDD. In particular, we sought to understand how novice and professional software developers, arranged in pairs (a driver and a pointer), perceive and apply TDD. Method: 14 novice software developers, i.e., graduate students in Computer Science at the University of Basilicata, and six professional software developers (with one to 10 years work experience) participated in our ethnographicallyinformed study. We asked the participants to implement a new feature for an existing software written in Java. We immersed ourselves in the context of the study, and collected data by means of contemporaneous field notes, audio recordings, and other artifacts. Results: A number of insights emerge from our analysis of the collected data, the main ones being: (i) refactoring (one of the phases of TDD) is not performed as often as the process requires and it is considered less important than other phases, (ii) the most important phase is implementation, (iii) unit tests are almost never up-to-date, (iv) participants first build a sort of mental model of the source code to be implemented and only then write test cases on the basis of this model; and (v) apart from minor differences, professional developers and students applied TDD in a similar fashion. Conclusions: Developers write quick-and-dirty production code to pass the tests and ignore refactoring.Copyright is held by the owner/auther(s)