Origin of the anomalies: the modified Heisenberg equation

Abstract

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 invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this approach is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.Comment: 7 pages, LaTe