  We prove a few spectral theorems for the density of states of a Weyl node
with arbitrary topology. We show that the density of extended states of a Weyl
node with random impurity potentials remains gapless in the presence of a
magnetic field. Therefore, a magnetic field precludes Anderson localization in
Weyl semi-metals, when inter-node transitions are suppressed for smooth enough
potentials. We also provide a rigorous quantum mechanical proof of the chiral
magnetic effect for arbitrary topology of a Weyl node.
