  An unbounded massless Dirac model with two nondegenerate Dirac cones is the
simplest model for Weyl semimetals, which show the anomalous electromagnetic
response of chiral magnetic effect (CME) and anomalous Hall effect (AHE).
However, if this model is naively used to analyze the electromagnetic response
within a linear response theory, it gives the result apparently inconsistent
with the persuasive prediction based on a lattice model. We show that this
serious difficulty is related to the breaking of current conservation in the
Dirac model due to quantum anomaly and can be removed if current and charge
operators are redefined to include the contribution from the anomaly. We
demonstrate that the CME as well as the AHE can be properly described using
newly defined operators, and clarify that the CME is determined by the
competition between the contribution from the anomaly and that from low-energy
electrons.
