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Casimir energy and the cosmologicai constant // Tomsk State Pedagogical University Bulletin. 2004. Issue 7 (44). P. 72-80

We regard the Wheeier-De Witt equation as a Sturm-Liouville problem with the cosmologicai constant considered as the associated eigenvalue. The used method to study such a problem is a variational approach with Gaussian trial wave functionate. We approximate the equation to one loop in a Schwarzschild background. A zeta function reguiarization is involved to handle with divergences. The reguiarization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormallzation procedure is introduced to remove the infinities together with a renormalization group equation.