  In this work we analyze the low energy nonrelativistic limit of Dirac theory
in the framework of effective field theory. By integrating out the high energy
modes of Dirac field, given in terms of a combination of the two-components
Weyl spinors, we obtain a low energy effective action for the remaining
components, whose equation of motion can then be compared to the
Pauli-Schr\"odinger equation after demanding normalization of the wave
function. We then discuss the relevance of the terms in the effective action in
the context of an anisotropic dimensional analysis which is suitable for
nonrelativistic theories.
