Geometry of Winter Model

TL;DR

This paper explores the geometric structure of the Winter model's Riemann surface to understand resonance phenomena, deriving both perturbative and non-perturbative results for observables in the weak-coupling regime.

Contribution

It introduces a geometric approach to analyze the Winter model, revealing the limitations of perturbation theory and providing explicit non-perturbative results.

Findings

Determines the resonance structure via Riemann surface construction.

Identifies the limitations of perturbation theory in the model.

Provides explicit non-perturbative results for weak-coupling observables.

Abstract

By constructing the Riemann surface controlling the resonance structure of Winter model, we determine the limitations of perturbation theory. We then derive explicit non-perturbative results for various observables in the weak-coupling regime, in which the model has an infinite tower of long-lived resonant states. The problem of constructing proper initial wavefunctions coupled to single excitations of the model is also treated within perturbative and non-perturbative methods.