  The quantum anomaly can be written alternatively into a form violating
conservation laws or as non-gauge invariant currents seen explicitly on the
example of chiral anomaly. By reinterpreting the many-body averaging, the
connection to Pauli-Villars regularization is established which gives the
anomalous term a new interpretation as arising from quantum fluctuations by
many-body correlations at short distances. This is exemplified by using an
effective many-body quantum potential which realizes quantum Slater sums by
classical calculations. It is shown that these quantum potentials avoid the
quantum anomaly but approaches the same anomalous result by many-body
correlations. A measure for the quality of quantum potentials is suggested to
describe these quantum fluctuations in the mean energy. Consequently quantum
anomalies might be a short-cut way of single-particle field theory to account
for many-body effects. This conjecture is also supported since the chiral
anomaly can be derived by a completely conserving quantum kinetic theory.
