A calculation of the Casimir force on a circular boundary
- 1 December 1981
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (12) , 2968-2973
- https://doi.org/10.1063/1.524859
Abstract
The zero point energy of a three-dimensional scalar field in the presence of a circular boundary of radius R is calculated using a Green’s function method. It is found that the energy is cutoff-dependent. The cutoff-dependent terms are explicitly calculated in terms of the geometry of the problem. It is found that E(ω0) = + 0.045/2R + (S/4π) ω20 −[(1/256)] ℱc2(s) ds] lnω0R, where S is the length of circular boundary (S = 2πR), c(s) the curvature of the boundary [c(s) = 1/R], and ω0 is the cutoff frequency.Keywords
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