Second Renormalization in the Casimir Energy Calculation with Subtraction of Similar Configurations in Curved Space

Subject Areas : Nonlinear Vibration

Madad Ali  Valuyan ¹ (دانشگاه آزاد اسلامی واحد سمنان - عضو هیات علمی)

Received: 2016-10-27 Accepted : 2016-10-30 Published : 2014-08-23

Keywords: frequency, Casimir Energy, Vacuum Polarization, Curved Space, Renormalization,

Abstract :

In this paper we investigate the Casimir energy for systems with Periodic Boundary Conditions (PBCs) on a two dimensional sphere (S^2) by Similar Configurations Subtraction Scheme (SCSS). The SCSS is a slight modification of Boyer's subtraction method to remove divergences which led to the bare parameters in the Casimir energy calculation. In this paper we first use this method for a problem in a curved space-time. For more simplicity we purpose a system with PBCs on a sphere with radius a and its scalar curvature R=2a^(-2). Usually, in the SCSS to remove divergences from zero point energy expressions, two comparable configurations have been designed and then the zero point energies of these two configurations are subtracted from each other. This setup for configurations made us an ability to divide divergences clearly and it would be to show all divergences are removed without resorting to any other techniques such as analytic continuation techniques. In final we compare our results with those reported in the literature, which are obtained from other regularization techniques.