Abstract
We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable truncation schemes for real-time calculations as well as the numerical procedure to self-consistently solve the flow equations for the spectral function. Subsequently, we discuss the relations to other perturbative and non-perturbative approaches to calculate spectral functions, and present a detailed comparison and benchmark in $d=0+1$ dimensions.
Highlights
Spectral functions of quarks, gluons, and the gauge invariant states of QCD are important ingredients in the theoretical description of heavy ion collisions performed at RHIC and LHC
After defining a d þ 1 dimensional regulator scheme that respects time-ordering on the SK contour, we introduce a diagrammatic notation simplifying the derivation of flow equations for n-point functions
We have presented an overview over on how to employ the functional renormalization group approach on the Schwinger-Keldysh contour to extract real-time spectral functions for scalar theories
Summary
Gluons, and the gauge invariant states of QCD are important ingredients in the theoretical description of heavy ion collisions performed at RHIC and LHC. Our knowledge about spectral properties of thermal QCD matter comes primarily from calculations in low energy effective theories of QCD, based on a variety of different techniques including (resummed) perturbative calculations [6,7,8] as well as nonperturbative functional approaches [9,10,11,12,13,14]. We adopt a real-time FRG approach on the Schwinger-Keldysh (SK) contour [26,27,28,29,30,31,32,33,34,35,36] to extract spectral functions in the OðNÞ model without the need for analytical continuation. Several appendices contain additional details intended for the nonexpert reader
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