Approaches to the Inverse Problem

TL;DR

This paper reviews recent theoretical and algorithmic advancements in solving the inverse problem of analytical continuation in lattice gauge theories, emphasizing Bayesian and Backus-Gilbert methods for non-perturbative studies.

Contribution

It provides a comprehensive review of recent developments in inverse problem techniques, highlighting variations of Bayesian and Backus-Gilbert methods.

Findings

Enhanced algorithms for analytical continuation

Improved non-perturbative predictions from lattice simulations

New avenues for Standard Model studies

Abstract

The analytical continuation of correlation functions from imaginary to real time is a crucial step in lattice gauge theories, and it challenges our ability to derive non-perturbative predictions from lattice simulations. We review aspects of this "inverse problem", which has driven both theoretical and algorithmic advancements in recent years, opening new promising avenues for non-perturbative studies of the Standard Model and beyond. The focus of this proceeding will be on variations of Backus-Gilbert and Bayesian methods.