ANOMALIES AND MIXED STATES

Abstract

There are many examples of quantum anomalies of continuous and discrete classical symmetries. Examples come from chiral anomalies in the Standard Model and gravitational anomalies in string theories. They occur when classical symmetries do not preserve the domains of quantum operators like the Hamiltonian. Here we show by a simple example, a particle on a circle, that anomalous symmetries can often be implemented at the expense of working with mixed states.