New insights into the analytic structure of correlation functions via kinetic theory

The way a relativistic system approaches fluid dynamical behavior can be understood physically through the signals that will contribute to its linear response to perturbations. What these signals are is captured in the analytic structure of the retarded correlation function. The nonanalyticities can be grouped into three types based on their dimension in the complex frequency plane. In this paper, we will use kinetic theory in the (momentum-dependent) relaxation time approximation to find how we can calculate their corresponding signals. In the most general case of a system with particles that have a continuum of thermalization rates, we find that a nonanalytic region appears. To calculate its signal, we introduce the “nonanalytic area density” that describes the properties of this region, and we construct a method to calculate it. Further, to take into account the ambiguity present in signal analysis, following from manipulations of the nonanalyticities, we will identify two specific choices called “pictures” with interesting analytic properties and compare in what scenarios each picture is most useful. Published by the American Physical Society 2024