Absence of equilibrium chiral magnetic effect

Understand

We analyse the $3+1$ D equilibrium chiral magnetic effect (CME).

• We apply derivative expansion to the Wigner transform of the two - point Green function.
• This technique allows us to express the response of electric current to external electromagnetic field strength through the momentum space topological invariant.
• We consider the wide class of the lattice regularizations of quantum field theory (that includes, in particular, the regularization with Wilson fermions) and also certain lattice models of solid state physics (including those of Dirac semimetals).