Zeta-function approach to Casimir energy with singular potentials

Details Zeta-function approach to Casimir energy with singular potentials Zeta-function approach to Casimir energy with singular potentials

2005-11-03

arxiv.org/abs/hep-th/0511038v2

Phys.Rev. D73 (2006) 025003

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 2 figures, added reference, address corrected

Scientific paper

10.1103/PhysRevD.73.025003

In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which are peculiar to the potentials. It is suggested to renormalize the energy using the condition that the energy of infinitely separated potentials is zero which corresponds to subtraction all terms of asymptotic expansion of zeta-function. The energy obtained in this way obeys all physically reasonable conditions. It is finite in the Dirichlet limit and it may be attractive or repulsive depending on the strength of potential. The effective action is calculated and it is shown that the surface contribution appears. The renormalization of the effective action is discussed.

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