  In this Comment we point out (i) that the Hamiltonian, Eq. (17) in the
Letter(Phys. Rev. Lett. 108, 070405 (2012)), is not a relativistic Hamiltonian,
(ii) then that the conditions in the Letter are irrelevant for a topological AC
and SAB effects, and (iii) conclusively that the non-relativistic Hamiltonian
employed by Peshkin and Lipkin (Phys. Rev. Lett. 74, 2847 (1995)) has the same
$U(1)_{mm}$ gauge structure for a fixed spin and then is not wrong, but their
incorrect interpretation of the spin autocorrelations led to the incorrect
conclusion.

Mesoscale and Nanoscale Physics;Quantum Physics