  The role of the contribution from the fermion mass term in the axial vector
Ward identity in generating the U(1) axial anomaly, both local and global, is
elucidated. Gauge invariance requires the fermion to decouple from the gauge
field if it is very heavy. This identifies the Adler-Bell-Jackiw (ABJ) anomaly
with the asymptotic limit of the sign reversed mass term. In an instanton
background, the chiral limit $(m = 0)$ of the mass term does not vanish but
consists of contributions from fermion zero modes. Space time integral of these
zero mode contributions exactly cancels, thanks to the Atiyah-Singer index
theorem, the integral of the ABJ anomaly and suggests that the Jacobian for
global U(1) chiral transformation is trivial even in an instanton background.
This can be realised in the representation of the fermion partition function in
a Weyl basis. The resolution of the strong CP problem is thus achieved in an
axionless physical world. In chiral gauge theories the fermion partition
function admits of a gauge invariant representation but only at the cost of
locality. Implementation of fermion averaging of the gauge current with the
invariant partition function yields the current whose covariant derivative is
the covariant anomaly. With the covariant current as input one can derive an
integrable current whose covariant derivative is the minimal consistent anomaly
obeying the Wess-Zumino consistency condition. The distinction between the two
currents disappears if either the covariant or the consistent anomaly vanishes.
This is realised only if the fermion belongs to an anomaly-free representation
of the gauge group.
