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.
Perturbative expansion in the Galilean-invariant spin-1/2 Chern-Simons field theory
A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-1/2 fields of distinct masses M and M{sup {prime}}. A method for the construction of states containing N particles of mass M and N{sup {prime}} particles of mass M{sup {prime}} is given which is subsequently used to display equivalence to the spin-1/2 Aharonov-Bohm effect in the N=N{sup {prime}}=1 sector of the model. The latter is then studied in perturbation theory to determine whether there are divergences in the fourth order (one-loop) diagram. It is found that the contribution of that order is finite (and vanishing) for the case of parallel spin projections while the antiparallel case displays divergences which are known to characterize the spin-0 case in field theory as well as in quantum mechanics. {copyright} {ital 1997} {ital The American Physical Society}
Tradeoffs and limitations in statistically based image reconstruction problems.
TRADEOFFS AND LIMITATIONS IN STATISTICALLY BASED IMAGE RECONSTRUCTION PROBLEMS