Casimir Energy of the Massless Scalar Field on S-1 by the Point-Splitting Method

Authors: Selçuk S. BAYIN, J. P. KRISCH, Mustafa ÖZCAN

Abstract: 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.