  The effective Lagrangian for \eta' incorporating the effect of the QCD
\theta-angle has been developed previously. We revisit this Lagrangian and
carry out its canonical quantization with particular attention to the test
function spaces of constraints and the topology of the \eta'-field. In this
way, we discover a new chirally symmetric coupling of this field to chiral
multiplets which involves in particular fermions. This coupling violates P and
T symmetries. In a subsequent paper, we will evaluate its contribution to the
electric dipole moment (EDM) of fermions. Our motivation is to test whether the
use of mixed states restores P and T invariance, so that EDM vanishes. This
calculation will be shown to have striking new physical consequences.
