Certified spectral functions from Euclidean correlators

by Dr Sophie Mutzel (Paris, Ecole des Mines)

Tuesday 27 Oct 2026, 16:00 → 17:00 Europe/Zurich

4/2-037 - TH meeting room (CERN)

In many non-perturbative approaches to relativistic quantum field theory, one has direct access only to Euclidean correlation functions of local operators. Extracting dynamical information, such as the spectral density, from these data amounts to solving an inverse Laplace transform, an inherently ill-posed problem.

Building on the approach of Lawrence (arXiv:2408.11766), we develop a convex optimization framework that combines spectral positivity with constraints from Euclidean correlators. We show how the dual formulation can be relaxed into a hierarchy of finite linear or semidefinite programs, solvable with standard solvers and enjoying rigorous convergence guarantees. These programs yield certified bounds on spectral observables and real-time correlation functions compatible with the Euclidean data under a specified error model. 

I will illustrate the framework using Monte Carlo data with statistical errors. In some cases, infeasibility certificates can reject a proposed statistical error model at a chosen confidence level, for example when uncertainties have been underestimated.