  Some free--field spectral problems on a generalised cylinder are revisited.
In two dimensions, conformal scalar effective actions for various boundary
conditions are written in elliptic function terms and some special values
given. Fermions are then discussed in arbitrary dimensions and an analysis of
the most general local (`bag') boundary conditions is given leading to an
intrinsic formula for the eigenvalues which interpolate between Neveu--Schwarz
and Ramond. This is used to give reasonably explicit expressions for the
effective action and other values of the zeta function. It is shown that these
boundary conditions are transferred as a chemical potential to the boundary
spectral problem. The existence of real exponential eigenmodes along the
cylinder is pointed out and a curious asymmetry between the positive and
negative Dirac spectra uncovered for large cylinder length.
