Casimir Energy of the Massless Scalar Field on S-1 by the Point-Splitting Method
We calculate the Casimir energy of the massless scalar field on a one dimensional Riemann sphere (S-1) using the point-splitting method. We consider the full space, half space and an arc of arbitrary radius. This problem is interesting since it may be solved analytically be several renormalization techniques.
BAYIN, Selçuk S.; KRISCH, J. P.; and ÖZCAN, Mustafa (1997) "Casimir Energy of the Massless Scalar Field on S-1 by the Point-Splitting Method," Turkish Journal of Physics: Vol. 21: No. 4, Article 10. Available at: https://journals.tubitak.gov.tr/physics/vol21/iss4/10