Finite temperature Casimir effect on spherical shells in (D+1)-dimensional spacetime and its high temperature limit

Abstract

We consider the finite temperature Casimir free energy acting on a spherical shell in (D+1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar and electromagnetic fields. Dirichlet, Neumann, perfectly conducting and infinitely permeable boundary conditions are considered. The Casimir free energy is regularized using zeta functional regularization technique. To renormalize the Casimir free energy, we compute the heat kernel coefficients $c_n$, $0\le n\le D+1$, from the zeta function $\zeta (s)$. After renormalization, the high temperature leading term of the Casimir free energy is $-c_{D}T\ln T-T{\zeta }^{\prime }(0)/2$. Explicit expressions for the renormalized Casimir free energy and ${\zeta }^{\prime }(0)$ are derived. The dependence of the renormalized Casimir free energy on temperature is shown graphically.

28 pages, 8 figures

References in corpus (4)

• Thermal Casimir effect in ideal metal rectangular boxes
• Recent Developments in the Casimir Effect
• Casimir effect of electromagnetic field in D-dimensional spherically symmetric cavities
• Electromagnetic Casimir effect on the boundary of a D-dimensional cavity and the high temperature asymptotics

Cited by in corpus (5)

• Magnetic field corrections to the repulsive Casimir effect at finite temperature
• Exact classical sphere-plate Casimir interaction in (D+1)-dimensional spacetime
• Finite temperature Casimir interaction between spheres in $(D+1)$-dimensional spacetime: Exact computations and asymptotic expansions
• Virial coefficients expressed by heat kernel coefficients
• Spherical Casimir effect for a massive scalar field on the three dimensional ball