Casimir energy in the axial gauge - art. no. 085027

The zero-point energy of a conducting spherical shell is studied by imposin g the axial gauge via path-integral methods, with boundary conditions on th e electromagnetic potential and ghost fields. The coupled modes are then fo und to be the temporal and longitudinal modes for the Maxwell field. The re sulting system can be decoupled by studying a fourth-order differential equ ation with boundary conditions on longitudinal modes and their second deriv atives. The exact solution of such an equation is found by using a Green-fu nction method, and is obtained from Bessel functions and definite integrals involving Bessel functions. Complete agreement with a previous path-integr al analysis in the Lorenz gauge, and with Boyer's value, is proved in detai l.