Non Relativistic Limit in QFT: a Wilson Renormalization Group Approach in the Minkowski Space
We study the non relativistic limit of a model of fermions interacting through a Chern-Simons field, from a perspective that resembles the Wilson Renormalization Group (WRG) approach. The main difference of our approach to WRG is that instead of working in the Euclidean space, we directly work in Minkowski space. For the nonrelativistic limit this procedure admits a more direct interpretation of the results. As we will see, this modified WRG approach solves some difficulties, and gives a new understanding of non relativistic models that are not clear in the usual "classical" nonrelativistic (CNR) limit found in most text books. The method is general and our choice of the Chern-Simons as the gauge field is only for the sake of simplicity of illustration.
Differential regularization of a nonrelativistic anyon model.
Differential regularization is applied to a field theory of a nonrelativistic charged boson field [phi] with [lambda]([phi][sup *][phi])[sup 2] self-interaction and coupling to a statistics-changing U(1) Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the [phi][sup *][phi][sup *][phi][phi] four-point function, which is the only primitively divergent Green's function, are obtained up to three-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the [beta] function is investigated. If the renormalization scheme is fixed to agree with a previous one-loop calculation, the two- and three-loop contributions to [beta]([lambda],[ital e]) vanish, and [beta]([lambda],[ital e]) itself vanishes when the self-dual'' condition relating [lambda] to the gauge coupling [ital e] is imposed.
Relativistic corrections to the Aharonov-Bohm scattering
Abstract We determine the ¦ p ¦/ m expansion of the two-body scattering amplitude of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. It is shown that the existence of a critical value of the selfinteraction parameter for which the two-particle amplitude reduces to the Aharonov-Bohm one is restricted to the leading, nonrelativistic, order. The subdominant terms correspond to relativistic corrections to the Aharonov-Bohm scattering.