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The analytic renormalization group

By Frank Ferrari

Abstract

Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0), together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples

Topics: Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Publisher: Elsevier
Year: 2016
DOI identifier: 10.1016/j.nuclphysb.2016.06.003
OAI identifier: oai:doaj.org/article:c8beb018ddbe4846b08c98f4dd1d3522
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