Abstract
We present first results on the calculation of fermionic spectral functions from analytically continued flow equations within the Functional Renormalization Group approach. Our method is based on the same analytic continuation from imaginary to real frequencies that was developed and used previously for bosonic spectral functions. In order to demonstrate the applicability of the method also for fermionic correlations we apply it here to the real-time quark propagator in the quark-meson model and calculate the corresponding quark spectral functions in the vacuum.
Highlights
The spectral properties of strongly interacting matter under extreme conditions, as encountered in the early Universe and compact stellar objects, are of fundamental importance for identifying the relevant degrees of freedom in the equation of state and respective transport properties
We present first results on the calculation of fermionic spectral functions from analytically continued flow equations within the functional renormalization group approach
Our method is based on the same analytic continuation from imaginary to real frequencies that was developed and used previously for bosonic spectral functions
Summary
The spectral properties of strongly interacting matter under extreme conditions, as encountered in the early Universe and compact stellar objects, are of fundamental importance for identifying the relevant degrees of freedom in the equation of state and respective transport properties. Spectral functions are real-time quantities, while the underlying equilibrium state is commonly obtained from imaginary-time (Euclidean) evaluations of the partition function In this setting, a thermodynamically consistent computation of the spectral properties poses a major challenge since analytic continuations of the pertinent Euclidean n-point functions are required. Reconstruction methods (see e.g., [8,9]), we perform the analytic continuation on the level of the FRG flow equations for retarded two-point correlation functions which are solved directly in the corresponding domain of frequencies close to the real axis. For the first time we here present a FRG calculation of fermionic spectral functions obtained from analytically continued flow equations which can be solved numerically.
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