High Energy Physics - Lattice
[Submitted on 23 Feb 2016 (v1), last revised 16 Aug 2016 (this version, v2)]
Title:The Analytic Renormalization Group
View PDFAbstract:Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients $G_{k}$, $k\in\mathbb Z$, associated with the Matsubara frequencies $\nu_{k}=2\pi k/\beta$. We show that analyticity implies that the coefficients $G_{k}$ must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct "Analytic Renormalization Group" linear maps $\mathsf A_{\mu}$ which, for any choice of cut-off $\mu$, allow to express the low energy Fourier coefficients for $|\nu_{k}|<\mu$ (with the possible exception of the zero mode $G_{0}$), together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for $|\nu_{k}|\geq\mu$. Operating a simple numerical algorithm, we show that the exact universal linear constraints on $G_{k}$ 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.
Submission history
From: Frank Ferrari [view email][v1] Tue, 23 Feb 2016 23:34:53 UTC (6,492 KB)
[v2] Tue, 16 Aug 2016 16:33:29 UTC (6,492 KB)
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