Perfect magnetic conductor Casimir piston ind+1dimensions

Abstract

Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC's and Casimir experiments involving structures that approximate PMC's may be carried out in the not too distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in d + 1 dimensions. The PMC Casimir energy is explicitly evaluated by summing over p + 1-dimensional Dirichlet energies where p ranges from 2 to d inclusively. We derive two exact d-dimensional expressions for the Casimir force on the piston and find that the force is negative (attractive) in all dimensions. Both expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from our work is a contribution to the PEC literature: we obtain a useful alternative expression for the PEC Casimir piston in 3+1 dimensions and also evaluate the Casimir force per unit area on an infinite strip, a geometry of experimental interest. *

Kaluza-Klein models as pistons

“…Imposing Dirichlet boundary conditions, as L → ∞ it is shown that the piston is attracted to the nearest end of the box. Higher-dimensional pistons have been considered with various boundary conditions [11,14,28,29,38,39,42]. Hertzberg et al showed that in three dimensions for perfect metallic boundary conditions the rectangular piston is attracted to the closest base [28,29]; for pistons with rectangular cross sections and Dirichlet or Neumann boundary conditions see also [11,12].…”

Casimir Pistons With Curved Boundaries

“…Before closing this section let us briefly comment on the regularization dependence of the force corresponding to the pistons we used. We shall make use of a cutoff parameter λ in the Casimir energy, in order to see explicitly the cancellation of the surface terms we mentioned in the introduction [11,25,27,26,16,17,18,19]. We work again for the piston 2 configuration.…”

“…However there is no reason to justify the loss of the surface term within the cutoff regularization technique. The Casimir piston solves this problem in a very nice way, because the surface terms of the two piston chambers cancel and thus the Casimir force can be consistently calculated [8,25,27,26,7,3,2,10,16,17,18,19]. We shall use the zeta-function regularization technique and also treat the problem numerically.…”

“…The boundary conditions on the 'plates' where Dirichlet. There exists a large literature on the subject [8,25,27,26,7,3,2,10,16,17,18,19] calculating the Casimir force for various piston configurations and for various boundary conditions of the scalar field. Also most results where checked at finite temperature.…”

Finite temperature Casimir effect and dispersion in the presence of compactified extra dimensions

“…We are led to a Casimir piston model in which spacetime is flat. This model has attracted considerable attention in the recent literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. One reason for the current interest is obviously the mathematical elegance of the formalism; the efficiency of regularization procedures like the zeta function regularization is quite striking.…”