Visualizing resonances in finite volume

TL;DR

This paper introduces an analytic continuation method to study resonance properties directly in finite volume by transforming finite volume Green's functions into their infinite volume counterparts, enabling more precise resonance analysis.

Contribution

It presents a novel approach using analytic continuation of finite volume Green's functions to extract resonance properties without requiring infinite volume calculations.

Findings

The method successfully maps finite volume Green's functions to infinite volume counterparts.

It allows direct study of resonance properties in finite volume dynamical equations.

The approach improves understanding of resonance behavior in lattice simulations.

Abstract

In present work, we explore and experiment an alternative approach of studying resonance properties in finite volume. By analytic continuing finite lattice size $L$ into complex plane, the oscillating behavior of finite volume Green's function is mapped into infinite volume Green's function corrected by exponentially decaying finite volume effect. The analytic continuation technique thus can be applied to study resonance properties directly in finite volume dynamical equations.