  In an attempt to understand a recently discovered torque anomaly in quantum
field theory with boundaries, we calculate the Casimir energy and torque of a
scalar field subject to Dirichlet boundary conditions on an annular sector
defined by two coaxial cylinders intercut by two planes through the axis. In
this model the particularly troublesome divergence at the cylinder axis does
not appear, but new divergences associated with the curved boundaries are
introduced. All the divergences associated with the volume, the surface area,
the corners, and the curvature are regulated by point separation either in the
direction of the axis of the cylinder or in the (Euclidean) time; the full
divergence structure is isolated, and the remaining finite energy and torque
are extracted. Formally, only the regulator based on axis splitting yields the
expected balance between energy and torque. Because of the logarithmic
curvature divergences, there is an ambiguity in the linear dependence of the
energy on the wedge angle; if the terms constant and linear in this angle are
removed by a process of renormalization, the expected torque-energy balance is
preserved.
