Noether Theorems and Quantum Anomalies

A quantum anomaly is the breaking of symmetry with respect to some transformations after the quantization of a classical Hamiltonian or Lagrangian system. It is shown that both the Noether theorems (including their infinite-dimensional versions) and the explanation of the origin of quantum anomalies can be obtained by using similar formulas for derivatives of functions whose values are measure in the former case and pseudomeasures in the latter.