  We discuss the construction and properties of rigidly-rotating states for
free scalar and fermion fields in quantum field theory. On unbounded Minkowski
space-time, we explain why such states do not exist for scalars. For the Dirac
field, we are able to construct rotating vacuum and thermal states, for which
expectation values can be computed exactly in the massless case. We compare
these quantum expectation values with the corresponding quantities derived in
relativistic kinetic theory.
