Exact renormalization group on point interactions

Abstract

The goal of this thesis is to present a non-perturbative renormalization of point interactions in non-relativistic quantum mechanics using Exact Renormalization Group (ERG) techniques. The analyzed model is a particle interacting with a Dirac-Delta potential on various two dimensional Riemannian Manifolds, namely the Euclid Plane R2, the Hyperbolic Plane H2, and the Sphere S2. In all cases the problem contains logarithmic divergences, hence regularization and renormalization are needed. The renormalization is performed using the ERG method, where one gets an expression for the ow equation of the effective coupling constant by integrating out degrees of freedom between the bare scale .. and the effective scale ... The main conclusion of this work is to show that the flow equations are identical in all three manifolds under consideration.