The Casimir Energy in a Separable Potential

Details The Casimir Energy in a Separable Potential The Casimir Energy in a Separable Potential

1999-07-27

arxiv.org/abs/hep-th/9907199v1

Annals Phys. 282 (2000) 432-448

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 4 EPS figures, REVTeX using BoxedEPS macros; email to jaffe@mit.edu

Scientific paper

10.1006/aphy.2000.6041

The Casimir energy is the first-order-in-\hbar correction to the energy of a time-independent field configuration in a quantum field theory. We study the Casimir energy in a toy model, where the classical field is replaced by a separable potential. In this model the exact answer is trivial to compute, making it a good place to examine subtleties of the problem. We construct two traditional representations of the Casimir energy, one from the Greens function, the other from the phase shifts, and apply them to this case. We show that the two representations are correct and equivalent in this model. We study the convergence of the Born approximation to the Casimir energy and relate our findings to computational issues that arise in more realistic models.

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