Double copy and the double Poisson bracket

TL;DR

This paper introduces a unified covariant framework for deriving field equations of Yang-Mills and gravity theories using a doubled Poisson bracket structure on ambitwistor spaces, linking algebraic structures to quantum diagrams.

Contribution

It formulates a novel covariant double Poisson bracket approach to derive fundamental field equations from ambitwistor phase spaces, suggesting a new algebraic perspective.

Findings

Unified formulation of Yang-Mills and gravity equations

Identification of a doubled Poisson bracket structure

Connection between ambitwistor space and kinematic algebra

Abstract

We derive first-order and second-order field equations from ambitwistor spaces as phase spaces of massless particles. In particular, the second-order field equations of Yang-Mills theory and general relativity are formulated in a unified form $\{\{H,H\}\}_\nabla = 0$, whose left-hand side describes a doubling of Poisson bracket in a covariant sense. This structure originates from a one-loop diagram encoded in gauge-covariant, associative operator products on the ambitwistor worldlines. A conjecture arises that the kinematic algebra might manifest as the Poisson algebra of ambitwistor space.