Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-01-19
Phys.Rev.D58:045003,1998
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, 2 figures, subm. to Phys. Rev
Scientific paper
10.1103/PhysRevD.58.045003
The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is calculated. The calculation is performed in the framework of covariant perturbation theory with the boundary conditions implemented as constraints. The formalism is briefly reviewed and its use is explained by deriving the known results for two parallel planes. The ultraviolet divergencies are shown to have the same structure as those for a massive field in zeroth order of $\alpha$. In the zeta-functional regularization employed by us no divergencies appear. If the radius of the sphere is large compared to the Compton wavelength of the electron the radiative correction is of order $\alpha/(R^2m_e)$ and contains a logarithmic dependence on $m_eR$. It has the opposite sign but the same order of magnitude as in the case of two parallel planes.
Bordag Michael
Lindig Joachim
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