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.
Low energy limit of the chern-simons theory coupled to fermions
Abstract We study the nonrelativistic limit of the theory of a quantum Chern–Simonsﬁeld minimally coupled to Dirac fermions. To get the nonrelativistic eﬀec-tive Lagrangian one has to incorporate vacuum polarization and anomalousmagnetic moment eﬀects. Besides that, an unsuspected quartic fermionicinteraction may also be induced. As a by product, the method we use to cal-culate loop diagrams, separating low and high loop momenta contributions,allows to identify how a quantum nonrelativistic theory nests in a relativisticone.I. INTRODUCTION Nonrelativistic quantum ﬁeld theories are important to the description and clariﬁcationof conceptual aspects of the physics of systems in the low energy regime. One example ofsuch situation is provided by the treatment of the Aharonov Bohm eﬀect [1] by means of themodel of a scalar ﬁeld minimally coupled to a Chern–Simons (CS) ﬁeld. In order to achieveaccordance between the exact and perturbative one loop calculations, it was necessary toinclude in the perturbative approach a quartic scalar self interaction with a coupling tuned1
Spin label motion in fatty acids.
Spin labels dissolved in highly purified fatty acid systems exhibit nearly identical tumbling rates in liquid and solid phases. Even though the spin labels do not have the same molecular geometry as the lipid matrix the melting point of the matrix can be inferred by measurements of the temperature dependency of molecular motion.