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 HorakSpeakerHeidelberg UniversityJan 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)
InstructorECT*My research interest lies in the field of phenomenological aspects of Quantum Chromodynamics. My current research focuses on studying the quark structure of hadrons, using the Dyson-Schwinger equations approach. Recently, I am working on the topics of form factors, distribution amplitude, parton distribution function and transverse momentum dependent distribution functions.