  The free quantum states of topologically massive electrodynamics and gravity
in 2+1 dimensions, are explicitly found. It is shown that in both theories the
states are described by infrared-regular polarization tensors containing a
regularization phase which depends on the spin. This is done by explicitly
realizing the quantum algebra on a functional Hilbert space and by finding the
Wightman function to define the scalar product on such a Hilbert space. The
physical properties of the states are analyzed defining creation and
annihilation operators.
  For both theories, a canonical and covariant quantization procedure is
developed. The higher order derivatives in the gravitational lagrangian are
treated by means of a preliminary Dirac procedure.
  The closure of the Poincar\'e algebra is guaranteed by the
infrared-finiteness of the states which is related to the spin of the
excitations through the regularization phase. Such a phase may have interesting
physical consequences.
