A kernel-derived orthogonal basis for spectral functions from Euclidean correlators

TL;DR

This paper introduces a systematic, prior-free orthogonal basis derived from the kernel of Euclidean correlators to better characterize spectral functions, aiding in the extraction of global features and constraints.

Contribution

It proposes a new orthogonal basis framework for spectral functions directly from the kernel, enhancing the extraction of spectral features without prior assumptions.

Findings

Captures global spectral features effectively.

Reproduces low-energy transport coefficients with good accuracy.

Serves as a preprocessing tool for spectral reconstruction.

Abstract

Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation functions constitutes a well-known ill-posed inverse problem and has motivated the development of numerous reconstruction techniques. In this work, we propose a systematic, prior-free framework for representing spectral functions using an orthogonal functional basis derived directly from the kernel of Euclidean two-point correlation functions. We identify a set of lattice-accessible constraints together with the associated basis functions. These functions can be reorganized into an orthogonal basis within which the spectral function may be approximated in a controlled manner. Using several model spectral functions, we demonstrate that the proposed expansion captures global spectral features and reproduces low-energy transport coefficients with good accuracy. While the numerical implementation requires high-precision Euclidean correlator data, the present framework is intended not as a direct reconstruction method, but rather as a tool for extracting robust constraints and overall spectral structures. The approach may therefore serve as a complementary ingredient or preprocessing step for existing spectral reconstruction techniques.