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arXiv · 2006.09778

Spectral functions in the $\phi^4$-theory from the spectral DSE

Jan Horak·Jan M. Pawlowski·Nicolas Wink
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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.

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Jan Horak, Jan M. Pawlowski, Nicolas Wink. 2020-06-17. Spectral functions in the $\phi^4$-theory from the spectral DSE. https://doi.org/10.1103/physrevd.102.125016

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