Green's function for a n-dimensional closed, static universe and with a spherical boundary

摘要

We construct the Hadamard Green's function by using the eigenfunction, whichare obtained by solving the wave equation for the massless conformal scalarfield on the S^n-1 of a n-dimensional closed, static universe. We also considerthe half space case with both the Dirichlet and the Neumann boundaryconditions. Solving of eigenfunction and eigenvalues of the corresponding fieldequation is interesting since the Casimir energy could be calculatedanalytically by various methods.