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In this study, the Casimir energy for massive scalar field with periodicboundary condition was calculated on spherical surfaces with $S^1$, $S^2$ and$S^3$ topologies. To obtain the Casimir energy on spherical surface, thecontribution of the vacuum energy of Minkowski space is usually subtracted fromthat of the original system. In large mass limit for surface $S^2$; however,some divergences would eventually remain in the obtained result. To removethese remaining divergences, a secondary renormalization program was manuallyperformed. In the present work, a direct approach for calculation of theCasimir energy has been introduced. In this approach, two similarconfigurations were considered and then the vacuum energies of theseconfigurations were subtracted from each other. This method provides morephysical meaning respect to the other common methods. Additionally, in largemass limit for surface $S^2$, it provides a situation in which the secondrenormalization program is automatically conducted in the calculationprocedure, and there was no need to do that anymore manually. Finally, byplotting the obtained values for the Casimir energy of the topologies andinvestigating their appropriate limits, the logic agreement between the resultsof our scheme and those of previous studies were discussed.

Casimir energy calculation for massive scalar field on spherical surfaces: an alternative approach