Effective field theory in time-dependent settings

TL;DR

This paper investigates how effective field theories can be constructed and interpreted in non-equilibrium, time-dependent systems using the Schwinger-Keldysh formalism, revealing new non-local terms affecting light field dynamics.

Contribution

It introduces a framework for deriving effective field theories in time-dependent settings and analyzes the emergence of non-local terms beyond the adiabatic approximation.

Findings

New non-local terms in the equations of motion for light fields

These terms vanish in the adiabatic limit

Implications for inflationary models and non-equilibrium dynamics

Abstract

We use the in-in or Schwinger-Keldysh formalism to explore the construction and interpretation of effective field theories for time-dependent systems evolving out of equilibrium. Starting with a simple model consisting of a heavy and a light scalar field taken to be in their free vacuum states at a finite initial time, we study the effects from the heavy field on the dynamics of the light field by analyzing the equation of motion for the expectation value of the light background field. New terms appear which cannot arise from a local action of an effective field theory in terms of the light field, though they disappear in the adiabatic limit. We discuss the origins of these terms as well as their possible implications for time dependent situations such as inflation.