Noether Theorems and Quantum Anomalies

J. Gough^a, T. S. Ratiu^b^,^c, and O. G. Smolyanov^d^,*
Translated by O. Sipacheva

^aInstitute of Mathematics, Physics and Computer Sciences, Aberystwyth University, Great Britain

^bSchool of Mathematics, Shanghai, Jiao Tong University, China

^cÉcole Polytechnique Fédérale de Lausanne, Switzerland

^dLomonosov Moscow State University, Moscow, Russia

Correspondence to: *e-mail: smolyanov@yandex.ru

Received 10 August, 2016

Abstract—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.

DOI: 10.1134/S1064562417010112