Abstract
We directly calculate spectral functions in the O(N)-model at finite temperature within the framework of the Functional Renormalization group. Special emphasis is put on a fully numerical framework involving four-dimensional regulators preserving Euclidean O(4) and Minkowski Lorentz invariance, an important prerequisite for future applications. Pion and sigma meson spectral functions are calculated for a wide range of temperatures across the phase transition illustrating the applicability of the general framework for finite temperature applications. In addition, various aspects concerning the interplay between the Euclidean and real time two-point function are discussed.
Highlights
The access to real-time correlation functions is key to the theoretical understanding of many interesting physics phenomena ranging from the bound-state spectrum of the theory at hand over decays to the dynamical evolution of both close-to- and far-from-equilibrium systems
Pion and sigma meson spectral functions are calculated for a wide range of temperatures across the phase transition illustrating the applicability of the general framework for finite temperature applications
The sigma meson emerges as a stable particle as Oð4Þ symmetry gets restored
Summary
The access to real-time correlation functions is key to the theoretical understanding of many interesting physics phenomena ranging from the bound-state spectrum of the theory at hand over decays to the dynamical evolution of both close-to- and far-from-equilibrium systems. We report on the progress within a fully numerical approach to directly compute real-time correlation functions introduced in [1,2] This formalism is based on the functional renormalization group (FRG) [3], a suitable nonperturbative method; see [4,5,6,7,8,9,10,11,12] for QCDrelated reviews. Our long-term goals are the hadron spectrum, transport coefficients, and other real-time observables within the framework of the fQCD Collaboration [62], which aims at a quantitative first-principle description of QCD from the FRG This stresses once more the importance of a fully numerical approach due to the sophisticated technical level already required at the Euclidean level to obtain quantitatively competitive results [43,45,46,47]. These quantities can be obtained conveniently from the spectral functions as demonstrated with the shear viscosity [56,57] from reconstructed spectral functions
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