Nonrelativistic reduction in quantum field theory

In this work we describe a nonrelativistic reduction process which relies directly on the evaluation of the ????????/m expansion of the quantum amplitudes in perturbation theory and which gets some inspiration from the theory of effective Lagrangians. These calculations are performed with the introduction of an intermediate cutoff which separates the contributions coming from low (L) and high (H) energy intermediate states and, as it is expected, the leading order of the expansion reproduces the result obtained with the corresponding nonrelativistic (NR) model while the sub dominant terms represent relativistic corrections. The reduction is made by identifying the L-contribution (in the leading order) with NR result which can be accomplished by a proper reinterpretation of the parameters involved. As specific applications, we consider the λ φ 4 theory in 2 + 1 dimensions and the scalar Chern-Simons theory from which one can derive relativistic corrections to the Aharonov-Bohn (AB) scattering - that can also be conceivable in a first quantized framework. (author)