  Different subtleties and problems associated with a nonrelativistic limit of
the field theory to the Schroedinger theory are discussed. In this paper, we
revisit different cases of the nonrelativistic limit of a real and complex
scalar field in the level of the Lagrangian and the equation of motion. We
develop the nonrelativistic limit of the Dirac equation and action in the way
that the nonrelativistic limit of spin-$\frac{1}{2}$ wave functions of
particles and antiparticles appear simultaneously. We study the effect of a
potential like $U(\phi)\propto \phi^4$ which can be attributed to axion dark
matter field in this limit. We develop a formalism for studying the
nonrelativistic limit of antiparticles in the quantum mechanics. We discussed
the non-local approach for the nonrelativistic limit and its problems.
