Nielsen–Ninomiya theorem states that in a lattice system one can not have just one chiral fermion. Fermions necessarily come in pairs of opposite chirality. I am wondering if one can "explain" this theorem using the following argument:
Since a Weyl crossing is a monopole of Berry curvature, following Dirac we should attach and unobservable solenoid to it (Dirac string), which necessarily ends on an antimonopole. Usually the end of the string can be put to infinity, but since the Brillouin zone is compact, we can not get rid of the antimonopole.
Do you think this is a correct way how to understand the Nielsen-Ninomiya theorem?