A Klein Gordon Particle Captured by Embedded Curves

TL;DR

This paper investigates a Klein-Gordon particle interacting with embedded curves on Riemannian manifolds, demonstrating the model's well-defined nature, finite ground state energy, and asymptotic freedom through heat kernel methods.

Contribution

It introduces a direct physical approach to analyze singular interactions on embedded curves, establishing renormalization and asymptotic properties of the model.

Findings

Renormalized problem is well-defined.

Ground state energy is finite and unique.

Model exhibits asymptotic freedom.

Abstract

In the present work, a Klein Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspective, via the heat kernel approach. It is shown that the renormalized problem is well-defined, and the ground state energy is unique and finite. The renormalization group invariance of the model is discussed, and it is observed that the model is asymptotically free.