We develop a non-perturbative functional framework for computing real-time correlation functionsin strongly correlated systems. The framework is based on the spectral representation of correlationfunctions and dimensional regularisation. Therefore, the non-perturbative spectral renormalisationsetup here respects all symmetries of the theories at hand. In particular this includes space-timesymmetries as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectralrenormalisation can be applied within general functional approaches such as the functional renor-malisation group, Dyson-Schwinger equations, and two- orn-particle irreducible approaches. As anapplication we compute the full, non-perturbative, spectral function of the scalar field in theφ4-theory in 2+1 dimensions from spectral Dyson-Schwinger equations. We also compute thes-channelspectral function of the fullφ4-vertex in this theory.


J. Horak and J. M. Pawlowski, N. Wink, “Spectral functions in the 4-theory from the spectral Dyson-Schwinger equations”, Phys. Rev. D 102, 125016 (2020).


Related to Project A02