Exact Renormalization Group for Point Interactions

TL;DR

This paper develops an exact renormalization group approach for point interactions in two-dimensional hyperbolic space, revealing insights into quantum systems with delta potentials in curved geometries.

Contribution

It extends the exact renormalization group method to nontrivial curved spaces, specifically hyperbolic geometry, for delta function potentials, a problem previously studied mainly in flat space.

Findings

Exact renormalization of delta potentials in hyperbolic space achieved

Demonstrates asymptotic freedom in a curved geometric setting

Provides a framework for analyzing quantum point interactions in nontrivial geometries

Abstract

Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble non-abelian gauge theories, yet it can be treated exactly in this nontrivial geometry.