Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Application of the Linear Momentum Equation01:15

Application of the Linear Momentum Equation

98
The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
The goal is to determine the force components in the x and y directions to hold the pipe in place. Since...
98
Momentum And Radiation Pressure01:20

Momentum And Radiation Pressure

2.0K
An object absorbing an electromagnetic wave would experience a force in the direction of propagation of the wave. This force occurs because electromagnetic waves contain and transport momentum. The force accounts for the wave's radiation pressure exerted on the object. Maxwell's prediction was confirmed in 1903 by Nichols and Hull by precisely measuring radiation pressures with a torsion balance. The measuring instrument had mirrors suspended from a fiber kept inside a glass container.
2.0K
Linear Momentum00:55

Linear Momentum

14.5K
The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum implies a tendency to continue on course—to move in the same direction; we tend to speak of sports teams or politicians gaining and maintaining the momentum to win.  Momentum is also associated with great mass and speed and is often considered when talking about collisions. For example, when rugby players collide and fall to the...
14.5K
Impulse-Momentum Theorem00:49

Impulse-Momentum Theorem

11.8K
The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called impulse, a vector quantity with the same direction as the total force acting on the object.
By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its...
11.8K
Moment-of-Momentum Equation01:09

Moment-of-Momentum Equation

129
The moment-of-momentum equation is a critical tool for analyzing the torque produced by the rotating blades of a wind turbine. This equation is derived by applying Newton's second law to a fluid particle, which states that the rate of change of linear momentum is equal to the external force acting on the particle.
129
Linear Momentum in Control Volume01:13

Linear Momentum in Control Volume

1.1K
Newton's second law is applied to obtain the linear momentum in a control volume in a fluid system. According to this law, the rate of change of linear momentum is equal to the sum of external forces acting on the system. When a control volume matches the fluid system at a specific moment, the forces acting on both are identical. Reynolds transport theorem helps explain this by breaking down the system's linear momentum into two components: the rate of change of linear momentum within...
1.1K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Transcriptomics of Diphyllatea (CRuMs) from South Pacific crater lakes confirm new cryptic clades.

The Journal of eukaryotic microbiology·2024
Same author

Amplitudes at Strong Coupling as Hyper-Kähler Scalars.

Physical review letters·2024
Same author

Lie polynomials and a twistorial correspondence for amplitudes.

Letters in mathematical physics·2021
Same author

The evolution of division of labour in structured and unstructured groups.

eLife·2021
Same author

All Order α^{'} Expansion of One-Loop Open-String Integrals.

Physical review letters·2020
Same author

Double-Copy Structure of One-Loop Open-String Amplitudes.

Physical review letters·2018
Same journal

On Point Spectrum of Jacobi Matrices Generated by Iterations of Quadratic Polynomials.

Communications in mathematical physics·2026
Same journal

A Mathematical Analysis of IPT-DMFT.

Communications in mathematical physics·2026
Same journal

Asymptotics of Symmetric Polynomials: A Dynamical Point of View.

Communications in mathematical physics·2026
Same journal

Commuting Quantum Operations Factorise.

Communications in mathematical physics·2026
Same journal

On the Open TS/ST Correspondence.

Communications in mathematical physics·2026
Same journal

A Superintegrable Quantum Field Theory.

Communications in mathematical physics·2026
See all related articles

Related Experiment Video

Updated: Jul 19, 2025

Blast Quantification Using Hopkinson Pressure Bars
09:41

Blast Quantification Using Hopkinson Pressure Bars

Published on: July 5, 2016

9.1K

A Lie Bracket for the Momentum Kernel.

Hadleigh Frost1, Carlos R Mafra2, Lionel Mason1

  • 1The Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Woodstock Rd, Oxford, OX2 6GG UK.

Communications in Mathematical Physics
|August 15, 2023
PubMed
Summary
This summary is machine-generated.

This study reveals that the S-map is a Lie bracket, enabling a generalized KLT map for tree-level scattering amplitudes. This provides an algebraic proof for gravity amplitude double pole cancellation and unifies various field theories.

More Related Videos

Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.5K
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

12.3K

Related Experiment Videos

Last Updated: Jul 19, 2025

Blast Quantification Using Hopkinson Pressure Bars
09:41

Blast Quantification Using Hopkinson Pressure Bars

Published on: July 5, 2016

9.1K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.5K
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

12.3K

Area of Science:

  • High Energy Physics
  • Quantum Field Theory
  • Mathematical Physics

Background:

  • Scattering amplitudes in quantum field theory are crucial for understanding particle interactions.
  • The color-kinematics duality and double copy provide powerful tools for amplitude computation.
  • Lie polynomials offer a novel algebraic structure for studying these amplitudes.

Purpose of the Study:

  • To investigate the double copy and tree-level color-kinematics duality for scattering amplitudes using Lie polynomials.
  • To establish a generalized KLT map and provide an algebraic proof for double pole cancellation in gravity amplitudes.
  • To explore Berends-Giele recursion for biadjoint scalar amplitudes and connect field theory amplitudes to Lie polynomial structures.

Main Methods:

  • Utilizing properties of Lie polynomials to analyze the S-map and establish its identity as a Lie bracket.
  • Developing a generalized KLT map from Lie polynomials and examining its matrix elements.
  • Applying Berends-Giele recursion to biadjoint scalar tree amplitudes within the Lie polynomial framework.
  • Characterizing field theory amplitudes via homomorphisms from the free Lie algebra to kinematic data.

Main Results:

  • The S-map is identified as a Lie bracket, leading to a generalized KLT map.
  • An algebraic proof for the cancellation of double poles in the KLT formula for gravity amplitudes is provided.
  • A unified framework for biadjoint scalar, Yang-Mills theory, and nonlinear sigma model amplitudes is established using Lie polynomial amplitudes.
  • The Bern-Carrasco-Johansson amplitude relations are shown to follow from the structural properties of Lie polynomial amplitudes.

Conclusions:

  • The study demonstrates the utility of Lie polynomials in understanding the double copy and color-kinematics duality.
  • The generalized KLT map and its connection to Lie brackets offer new insights into gravity amplitude structure.
  • The research provides a unified perspective on various field theories through the lens of Lie polynomial amplitudes.