The Analytic Renormalization Group
Frank Ferrari (UL Brussels, Intl. Solvay Inst., CERN)

TL;DR
This paper introduces the Analytic Renormalization Group, a set of universal linear equations derived from analyticity that relate low and high energy Fourier coefficients of finite temperature correlators, enabling improved data analysis.
Contribution
It formulates model-independent linear constraints on Fourier coefficients of finite temperature correlators and develops an algorithm to systematically refine approximate data sets using these constraints.
Findings
Universal linear equations relate Fourier coefficients across energy scales.
The method improves the accuracy of Monte Carlo simulation data.
Explicit examples demonstrate the effectiveness of the constraints.
Abstract
Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients , , associated with the Matsubara frequencies . We show that analyticity implies that the coefficients must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct "Analytic Renormalization Group" linear maps which, for any choice of cut-off , allow to express the low energy Fourier coefficients for (with the possible exception of the zero mode ), together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for . Operating a simple numerical algorithm, we show that the exact universal linear constraints…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
