# Scattering Amplitudes and the Navier-Stokes Equation

@article{Cheung2020ScatteringAA, title={Scattering Amplitudes and the Navier-Stokes Equation}, author={Clifford Cheung and James Mangan}, journal={arXiv: High Energy Physics - Theory}, year={2020} }

We explore the scattering amplitudes of fluid quanta described by the Navier-Stokes equation and its non-Abelian generalization. These amplitudes exhibit universal infrared structures analogous to the Weinberg soft theorem and the Adler zero. Furthermore, they satisfy on-shell recursion relations which together with the three-point scattering amplitude furnish a pure S-matrix formulation of incompressible fluid mechanics. Remarkably, the amplitudes of the non-Abelian Navier-Stokes equation also…

## 15 Citations

### Off-shell color-kinematics duality for Chern-Simons

- PhysicsJournal of High Energy Physics
- 2022

Abstract
Many gauge theories possess a hidden duality between color and kinematics in their on-shell scattering amplitudes. An open problem is to formulate an off-shell realization of the duality,…

### Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations

- Mathematics
- 2022

Recently, a non-abelian generalisation of the Navier-Stokes equation that exhibits a manifest duality between colour and kinematics has been proposed by Cheung and Mangan. In this paper, we offer a…

### Double copy for Lagrangians at trilinear order

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We present a novel double-copy prescription for gauge fields at the Lagrangian level and apply it to the original double copy, couplings to matter and the soft theorem. The Yang-Mills…

### On-shell correlators and color-kinematics duality in curved symmetric spacetimes

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We define a perturbatively calculable quantity — the on-shell correlator — which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the case of flat…

### Non-perturbative Double Copy in Flatland

- Physics
- 2022

We derive a non-perturbative, Lagrangian-level formulation of the double copy in two spacetime dimensions. Our results elucidate the ﬁeld theoretic underpinnings of the double copy in a broad class…

### Next-to-MHV Yang-Mills kinematic algebra

- MathematicsJournal of High Energy Physics
- 2021

Abstract
Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly…

### Symmetry and unification from soft theorems and unitarity

- Mathematics, PhysicsJournal of High Energy Physics
- 2021

Abstract
We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant,…

### Massive Covariant Colour-Kinematics in 3D

- Physics
- 2021

We explore topologically massive gauge theories using the covariant colour kinematics duality recently introduced in [1]. We show that the massive bi-adjoint scalar field is simply related to…

### Yang-Mills observables: from KMOC to eikonal through EFT

- PhysicsJournal of High Energy Physics
- 2022

We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through O α 2 $$ \mathcal{O}\left({\alpha}^2\right) $$ and to all orders in velocity. Our…

### The double copy of the multipole expansion

- Physics, Mathematics
- 2021

We consider the classical double copy, that relates solutions of biadjoint scalar, gauge and gravity theories. Using a recently developed twistor expression of this idea, we use wellestablished…

## References

SHOWING 1-10 OF 33 REFERENCES

### TASI Lectures on Scattering Amplitudes

- PhysicsAnticipating the Next Discoveries in Particle Physics
- 2018

These lectures are a brief introduction to scattering amplitudes. We begin with a review of basic kinematical concepts like the spinor helicity formalism, followed by a tutorial on bootstrapping…

### Annals of Physics 14

- 143
- 1961

### Phys

- Rev. Lett. 118, 121601
- 2017

### JHEP 06

- 118
- 2015

### Nuclear Physics B 306

- 759
- 1988

### Phys

- Rev. D 78, 085011
- 2008

### JHEP 02

- 095
- 2018

### JHEP 04

- 076
- 2008

### JHEP 12

- 003
- 2005