Abstract
In the framework of the functional renormalization group (FRG) we present a simple truncation scheme for the computation of real-time mesonic n-point functions, consistent with the derivative expansion of the effective action. Via analytic continuation on the level of the flow equations we perform calculations of mesonic spectral functions in the scalar O(N) model, which we use as an exploratory example. By investigating the renormalization-scale dependence of the 2-point functions we shed light on the nature of the sigma meson, whose spectral properties are predominantly of dynamical origin.
Highlights
Real-time observables in strongly interacting systems often pose major challenges for theoretical calculations
In this letter we study spectral functions of the elementary sigma and pion correlations in the O(N ) model with the functional renormalization group (FRG)
In the present work we have extended the truncation scheme of Refs. [13,14] for the functional renormalization group (FRG) equations of 2-point functions
Summary
Real-time observables in strongly interacting systems often pose major challenges for theoretical calculations. Real-time correlation functions are usually either reconstructed from their Euclidean analogs using Padé approximants or by maximum entropy methods They can be calculated directly in Minkowski spacetime by an analytical continuation at the level of the flow equations [13,14]. Spectral functions have been calculated with the FRG in non-relativistic models using different truncation schemes including the “BMW” approximation [24,25], vertex expansions or derivative expansions [26,27,28]. In all these cases, the spectral functions were reconstructed from Euclidean 2-point correlators via analytic continuation using Padé approximants. It is possible to extend the proposed approximation scheme to finite temperature and finite chemical potential or to include fermions [13, 14]
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