# On the absence of equilibrium chiral magnetic effect

Abstract : 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). It appears, that in these models the mentioned topological invariant vanishes identically at nonzero chiral chemical potential. That means, that the bulk equilibrium CME is absent in those systems.
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https://hal.archives-ouvertes.fr/hal-01275180
Contributor : Mikhail Zubkov <>
Submitted on : Friday, April 15, 2016 - 7:36:14 PM
Last modification on : Thursday, March 5, 2020 - 5:33:38 PM
Document(s) archivé(s) le : Saturday, July 16, 2016 - 2:01:12 PM

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• HAL Id : hal-01275180, version 3

### Citation

Mikhail Zubkov. On the absence of equilibrium chiral magnetic effect. Physical Review D, American Physical Society, 2016, D, 93 (10), pp.105036. ⟨hal-01275180v3⟩

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