Infrared Behavior of Interacting Quantum Field

Abstract

This chapter provides a pedagogical guide to research works on the infrared behavior of interacting quantum fields in de Sitter space which began in the 80s but has seen vibrant activities in the last decade. It aims to help orient readers who wish to enter into research into this area but are bewildered by the vast and diverse literature on the subject. We describe the three main veins of activities – the Euclidean zero-mode dominance, the Lorentzian interacting quantum field theory and the classical stochastic field theory approaches – in some detail, explaining the underlying physics and the technicalities of each. This includes the identification of zero mode in Euclidean quantum field theory, the use of 2PI effective action, the concept of effective infrared dimension, dimensional reduction, dynamical finite size effect, the late time behavior described by Langevin and Fokker–Planck equations, functional resummation techniques and nonperturbative renormalization group methods. We show how these approaches are interconnected, and highlight recent papers that hold promise for future developments.