Self-consistent Spectral Functions in the $O(N)$ Model from the FRG

Understand

We present the first self-consistent direct calculation of a spectral function in the framework of the Functional Renormalization Group.

• The study is carried out in the relativistic $O(N)$ model, where the full momentum dependence of the propagators in the complex plane as well as momentum-dependent vertices are considered.
• The analysis is supplemented by a comparative study of the Euclidean momentum dependence and of the complex momentum dependence on the level of spectral functions.
• This work lays the groundwork for the computation of full spectral functions in more complex systems.