Records from the S-Matrix Marathon: Schwinger-Keldysh Formalism

TL;DR

This paper reviews real-time quantum field theory techniques, focusing on the Schwinger-Keldysh formalism and its applications to holography and quantum scrambling, providing insights into out-of-time-order correlators and thermal observables.

Contribution

It offers a comprehensive overview of the Schwinger-Keldysh formalism, including its general principles, extensions, and holographic computation methods, with applications to open quantum systems and scrambling dynamics.

Findings

Clarifies the principles of the Schwinger-Keldysh formalism.

Describes holographic methods for thermal real-time observables.

Explains the role of out-of-time-order correlators in quantum scrambling.

Abstract

These notes provide an overview of real-time techniques in quantum field theories and holography. We outline the general rationale and principles underlying the Schwinger-Keldysh formalism and its out-of-time-order generalizations. To illustrate its broad utility we frame our discussion in the language of open quantum dynamics. As a specific application we describe how such real-time observables help in understanding scrambling dynamics. We also describe the holographic prescription for computing thermal Schwinger-Keldysh observables. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11-22 March 2024.