Abstract
We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation. Therefore, the non-perturbative spectral renormalisation setup 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. As an application we compute the full, non-perturbative, spectral function of the scalar field in the $\phi^4$-theory in $2+1$ dimensions from spectral Dyson-Schwinger equations. We also compute the $s$-channel spectral function of the full $\phi^4$-vertex in this theory.
Highlights
The study of the dynamics and resonance structure of strongly correlated systems requires the knowledge of realtime correlation functions
In this work. we develop a novel approach for the direct computation of real-time (Minkowski) observables that is based on spectral representations of correlation functions
We developed a spectral functional approach for the direct nonperturbative computation of real-time correlation functions
Summary
The study of the dynamics and resonance structure of strongly correlated systems requires the knowledge of realtime (timelike) correlation functions. Spectral functions encode the full, nonperturbative, information of the respective degrees of freedom and open the door to additional real-time quantities such as transport coefficients They are a useful tool when discussing resonances and bound states, since they give direct access to the spectrum of excitations in a given theory. We develop a novel approach for the direct computation of real-time (Minkowski) observables that is based on spectral representations of correlation functions. We apply our novel approach to the scalar φ4-theory in d 1⁄4 2 þ 1 dimensions This theory is a simple strongly correlated system and serves as a good benchmark for new techniques before applying them more involved theories such as non-Abelian ones.
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