Real-time Physics from Dyson-Schwinger Equations via Spectral Renormalisation

We set-up a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems via analytic continuation. The framework is based on the spectral representation of correlation functions and dimensional regularisation. Therefore, the non-perturbative spectral renormalisation set-up here respects all symmetries of the theories at hand. In particular, this includes space-time symmetries as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectral renormalisation can be applied within general functional approaches such as the functional renormalisation group, Dyson-Schwinger equations, and two- or n-particle irreducible approaches. First, this is applied to a scalar φ4-theory, where renormalised spectral DSEs are derived. Numerical results include the full, non-perturbative spectral function of the scalar field. Aiming at QCD on the long run, preliminary results indicate the existence of spectral representation of the gluon in Yang-Mills theory. There, a numerical gluon spectral function has been computed, which obeys the analytically known IR- und UV-asymptotics.


Moderator: Minghui Ding, ECT*


  • Jan Horak - Speaker
    Jan Horak: 2013 - 2017 Heidelberg University (Bachelor of Science, Thesis: Mono-X Collider Searches for Dark Matter) 2015 - 2016 San Diego State University 2017 - 2019 Heidelberg University (Master of Science, Thesis: Spectral Functions from Dyson-Schwinger Equations with Dimensional Regularization) 2020 - now: Heidelberg University (PhD, ongoing)


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