Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes

Abstract

Asymptotic observables in quantum field theory beyond the familiar $S$-matrix have recently attracted much interest, for instance in the context of gravity waveforms. Such observables can be understood in terms of Schwinger-Keldysh-type 'amplitudes' computed by a set of modified Feynman rules involving cut internal legs and external legs labelled by time-folds. In parallel, a homotopy-algebraic understanding of perturbative quantum field theory has emerged in recent years. In particular, passing through homotopy transfer, the $S$-matrix of a perturbative quantum field theory can be understood as the minimal model of an associated (quantum) $L_{\infty }$-algebra. Here we bring these two developments together. In particular, we show that Schwinger-Keldysh amplitudes are naturally encoded in an $L_{\infty }$-algebra, similar to ordinary scattering amplitudes. As before, they are computed via homotopy transfer, but using deformation-retract data that are not canonical (in contrast to the conventional $S$-matrix). We further show that the $L_{\infty }$-algebras encoding Schwinger-Keldysh amplitudes and ordinary amplitudes are quasi-isomorphic (meaning, in a suitable sense, equivalent). This entails a set of recursion relations that enable one to compute Schwinger-Keldysh amplitudes in terms of ordinary amplitudes or vice versa.

27 pages. Published version: typos corrected and the review in sec. 5.1 includes clarifying remarks

References in corpus (16)

• Black holes as mirrors: quantum information in random subsystems
• Double Copy from Homotopy Algebras
• CFT Unitarity and the AdS Cutkosky Rules
• Kinematic Lie Algebras From Twistor Spaces
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Holographic cameras: an eye for the bulk
• The Squeezed OTOC and Cosmology
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Cutting-Edge Tools for Cutting Edges
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Colour-kinematics duality, double copy, and homotopy algebras
• Symmetry Factors of Feynman Diagrams and the Homological Perturbation Lemma
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Higher Gauge Theory
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras

Cited by in corpus (1)

• Full S-matrices and Witten diagrams with (relative) L-infinity algebras