SCALAR CASIMIR EFFECT FOR A D-DIMENSIONAL SPHERE

The Casimir stress on a D-dimensional sphere (the stress on a sphere i s equal to the Casimir force per unit area multiplied by the area of t he sphere) due to the confinement of a massless scalar field is comput ed as a function of D, where D is a continuous variable that ranges fr om -infinity to infinity. The dependence of the stress on the dimensio n is obtained using a simple and straightforward Green's function tech nique. We find that the Casimir stress vanishes as D --> + infinity (D is a noneven integer) and also vanishes when D is a negative even int eger. The stress has simple poles at positive even integer values of D .