A Computation of the Casimir Energy on a Parallelepiped
Journal Title: Asian Research Journal of Mathematics - Year 2017, Vol 4, Issue 3
Abstract
The original computations deriving the Casimir energy and force consists of first taking limits of the spectral zeta function and afterwards analytically extending the result. This process of computation presents a weakness in Hendrik Casimir’s original argument since limit and analytic continuation do not commute. A case of the Laplacian on a parallelepiped box representing the space as the vacuum between two plates modelled with Dirichlet and periodic Neumann boundary conditions is constructed to address this anomaly. It involves the derivation of the regularised zeta function in terms of the Riemann zeta function on the parallelepiped. The values of the Casimir energy and Casimir force obtained from our derivation agree with those of Hendrik Casimir.
Authors and Affiliations
O. Omenyi, Louis
Keywords
Related Articles
- EP ID EP338470
- DOI 10.9734/ARJOM/2017/33689
- Views 76
- Downloads 0
Conditional Least Squares Estimation for Discretely Sampled Nonergodic Di usions
Strong consistency and conditional asymptotic normality of the conditional least squares estimator of a parameter appearing nonlinearly in the time dependent drift coefficient of the Itˆo stochastic differential equation...
MHD Oscillatory Flow of Jeffrey Fluid in an Indented Artery with Heat Source
In this article we studied blood flow through an indented artery and assumed blood to be Jeffrey fluid. The study investigates the influence of heat transfer on the flow profile of Jeffrey fluid in an indented artery. Al...
Arithmetic Operations on Heptagonal Fuzzy Numbers
In this paper we have introduced Heptagonal fuzzy numbers (HpFNs) which deals with the membership function for the set of seven numbers. Arithmetic operations such as addition, subtraction, multiplication and division of...
Hypothesis Testing for Fractional Stochastic Partial Di erential Equations with Applications to Neurophysiology and Finance
The paper obtains explicit form of fine large deviation theorems for the log-likelihood ratio in testing fractional stochastic partial differential equation models using a finite number of Fourier coefficients of the sol...
From Pascal Triangle to Golden Pyramid
We introduce a “structure” of epic proportions – golden pyramid whose sacred geometry is “Fibonacci squared”. In terms of mathematical beauty, the golden pyramid will perhaps be found to be comparable to Pascal triangle.