  The zero-point energy of a conducting spherical shell is studied by imposing
the axial gauge via path-integral methods, with boundary conditions on the
electromagnetic potential and ghost fields. The coupled modes are then found to
be the temporal and longitudinal modes for the Maxwell field. The resulting
system can be decoupled by studying a fourth-order differential equation with
boundary conditions on longitudinal modes and their second derivatives.
Complete agreement is found with a previous path-integral analysis in the
Lorenz gauge, and with Boyer's value. This investigation leads to a better
understanding of how gauge independence is achieved in quantum field theory on
backgrounds with boundary.
