Kaluza-Klein models as pistons

Abstract

We consider the influence of extra dimensions on the force in Casimir pistons. Suitable analytical expressions are provided for the Casimir force in the range where the plate distance is small, and that where it is large, compared to the size of the extra dimensions. We show that the Casimir force tends to move the center plate toward the closer wall; this result is true independently of the cross-section of the piston and the geometry or topology of the additional Kaluza-Klein dimensions. The statement also remains true at finite temperature. In the limit where one wall of the piston is moved to infinity, the result for parallel plates is recovered. If only one chamber is considered, a criterion for the occurrence of Lukosz-type repulsion, as opposed to the occurrence of renormalization ambiguities, is given; we comment on why no repulsion has been noted in some previous cosmological calculations that consider only two plates.

Casimir force between integrable and chaotic pistons

“…As already shown in Ref. [8,9], the smooth part of the spectrum gives the short distance behavior of the force between pistons, the leading term being the well known Proximity Force Approximation (PFA). Therefore, any signal of quantum chaos, if present, should pop out in the difference between the full Casimir force and its smooth part.…”

Expansion of infinite series containing modified Bessel functions of the second kind

“…Spectral zeta functions of the form (4.11) appear frequently in the literature, especially in the ambit of Kaluza-Klein theories, Casimir energy, and in the study of finite temperature effects in quantum field theory [4,9,10,21]. By utilizing the result obtained in (2.20) we find the following expression for the small-β expansion of the spectral zeta function in (4.11) 12) valid for all values of s. The expression (4.12) can be used to study the small-β behavior of quantities of interest.…”

Gluing Formula for Casimir Energies

“…We consider the configuration analyzed in, for example, [18,23]. Each chamber is assumed to have the structure…”

“…Many configurations, such as flat pistons at zero temperature [11][12][13][14][15][16][17][18][19][20] or finite temperatures [21][22][23][24], as well as curved pistons [25][26][27][28][29], have been analyzed on the basis of the spectrum of a Laplace-type operator associated with M 1 and M 2 . It is the aim of this article to introduce a completely new perspective on this type of analysis.…”