Chapter 2 Quantum Anomaly in Quantum Mechanics

In this chapter we learn about quantum anomaly of a symmetry in quantum mechanics, without assuming any kind of locality. Here, locality roughly means that we have a notion of “observables localized in a subregion of the space (or spacetime).” Both quantum field theory (QFT) and a quantum system on lattice are local in this sense, which affect the possible behavior of a symmetry. Here we will see what kind of “topological” phenomena are possible regarding symmetry when the locality is absent. In such case, we often regard that all of the observables are associated to a single point consisting the entire “space”, justifying to call such a system “0+1-dimensional.”