Origin of the anomalies: The modified Heisenberg equation

The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave the domain of definition of the Hamiltonian invariant and thus a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the nonconservation of the charges. This explanation is equivalent to that of Fujikawa in the path integral formalism. Finally, this approach is applied to conformal symmetry breaking in two-dimensional quantum mechanics.