Casimir energy of a semi-circular infinite cylinder

The Casimir energy of a semi-circular cylindrical shell is calculated by ma king use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symm etry axes of the cylinder and by considering only half of this configuratio n. All the surfaces, including the cutting plane, are assumed to be perfect ly conducting. The zeta functions for scalar massless fields obeying the Di richlet and Neumann boundary conditions on the semi-circular cylinder are c onstructed exactly. The sum of these zeta functions gives the zeta function for the electromagnetic field in question. The relevant plane problem is c onsidered also. In all the cases the final expressions for the correspondin g Casimir energies contain the pole contributions which are the consequence of the edges or corners in the boundaries. This implies that further renor malization is needed in order for the finite physical values for vacuum ene rgy to be obtained for given boundary conditions. (C) 2001 American Institu te of Physics.