In-In EFT

TL;DR

This paper develops an effective field theory framework specifically for In-In (real-time) correlators, establishing a formalism that aligns with full theory results and exploring connections to the Schrödinger representation of QFT.

Contribution

It constructs the EFT for In-In correlators, demonstrating the formal equivalence with In-Out functions and providing matching coefficients for operators with derivatives.

Findings

Matching coefficients for operators with derivatives are computed.

The Schrödinger representation naturally captures key features of In-In EFT.

The formalism ensures consistency between EFT and full theory for real-time correlators.

Abstract

The effective field theory (EFT) construction when the objects of interest are the In-In (or real time) correlators rather than the In-Out S-matrix elements is constructed. This is done using the formal equivalence between the In-In and In-Out correlation functions, and demanding that the EFT and the full theory provide the same answers for the In-In correlation functions. Matching coefficients for a simple example are provided including for operators with two or more space or time derivatives. It is also pointed out that the Schrodinger representation of QFT captures some of the desired features of these calculations in a natural way and may actually serve as a link between these calculations and the broader amplitude programme.