# Renormalization Analysis for Degenerate Ground States

## TL;DR

This paper analyzes how the ground state properties of a finite quantum system with degeneracies change analytically with coupling strength, using operator renormalization techniques under mild infrared conditions.

## Contribution

It extends operator theoretic renormalization methods to handle degenerate ground states in quantum systems coupled to relativistic bosons.

## Key findings

- Ground state projection and energy are analytic functions of coupling constant.
- Analyticity holds under mild infrared assumptions.
- Operator renormalization is successfully extended to degenerate cases.

## Abstract

We consider a Hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons. We show that the ground state projection and the ground state energy are analytic functions of the coupling constant in a cone with apex at the origin, provided a mild infrared assumption holds. To show the result operator theoretic renormalization is used and extended to degenerate situations.