  In statistical physics, useful notions of entropy are defined with respect to
some coarse graining procedure over a microscopic model. Here we consider some
special problems that arise when the microscopic model is taken to be
relativistic quantum field theory. These problems are associated with the
existence of an infinite number of degrees of freedom per unit volume. Because
of these the microscopic entropy can, and typically does, diverge for sharply
localized states. However the difference in the entropy between two such states
is better behaved, and for most purposes it is the useful quantity to consider.
In particular, a renormalized entropy can be defined as the entropy relative to
the ground state. We make these remarks quantitative and precise in a simple
model situation: the states of a conformal quantum field theory excited by a
moving mirror. From this work, we attempt to draw some lessons concerning the
``information problem'' in black hole physics
