747 research outputs found
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 where
is an interval of the real line and 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 . By exploiting zeta function
regularization techniques we provide formulas for the Casimir energy and force
involving the arbitrary warping function and base manifold .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
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 where is an interval of the real line and is a
compact, -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 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
-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 -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)
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