Spectral functions in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>-theory from the spectral Dyson-Schwinger equations
Jan Horak, Jan M. Pawlowski, Nicolas Wink
Abstract
We develop a nonperturbative 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 regularization. Therefore, the nonperturbative spectral renormalization 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 renormalization can be applied within general functional approaches such as the functional renormalization group, Dyson-Schwinger equations, and two- or $n$-particle irreducible approaches. As an application, we compute the full, nonperturbative, spectral function of the scalar field in the ${\ensuremath{\phi}}^{4}$-theory in $2+1$ dimensions from spectral Dyson-Schwinger equations. We also compute the $s$-channel spectral function of the full ${\ensuremath{\phi}}^{4}$-vertex in this theory.