Casimir Energy for Spherical boundaries

Abstract

Calculations of the Casimir energy for spherical geometries which are based on integrations of the stress tensor are critically examined. It is shown that despite their apparent agreement with numerical results obtained from mode summation methods, they contain a number of serious errors. Specifically, these include (1) an improper application of the stress tensor to spherical boundaries, (2) the neglect of pole terms in contour integrations, and (3) the imposition of inappropriate boundary conditions upon the relevant propagators. A calculation which is based on the stress tensor and which avoids such problems is shown to be possible. It is, however, equivalent to the mode summation method and does not therefore constitute an independent calculation of the Casimir energy.

Revtex, 7 pages, Appendix added providing details of failure of stress tensor method

References in corpus (3)

• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Simple method for calculating the Casimir energy for sphere
• Casimir Energy of a Spherical Shell

Cited by in corpus (7)

• QED with a spherical mirror
• Satellite Eötvös Test of the Weak Equivalence Principle for Zero-Point Vacuum Energy
• Comment on Casimir energy for spherical boundaries
• Boundary conditions at spatial infinity for fields in Casimir calculations
• Mesoscopic Casimir forces from effects of discrete particle number in the quantum vacuum
• On the corrections to the Casimir effect depending on the resolution of measurement
• Casimir effect for the sphere revisited