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

Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

6.7K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
6.7K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

951
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
951
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

3.7K
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
3.7K
Euler Equations of Motion01:19

Euler Equations of Motion

446
Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
446
Euler's Equations of Motion01:28

Euler's Equations of Motion

694
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
694
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

3.9K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
3.9K

You might also read

Related Articles

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

Sort by
Same author

Krylov Spread Complexity as Holographic Complexity beyond Jackiw-Teitelboim Gravity.

Physical review letters·2025
Same author

Quasinormal Modes of Nonthermal Fixed Points.

Physical review letters·2025
Same author

Geometric Interpretation of Timelike Entanglement Entropy.

Physical review letters·2025
Same author

The space of transport coefficients allowed by causality.

Nature physics·2024
Same author

Prescaling Relaxation to Nonthermal Attractors.

Physical review letters·2024
Same author

Rigorous Bounds on Transport from Causality.

Physical review letters·2023
Same journal

Critical points and syzygies for Feynman integrals.

Journal of high energy physics : JHEP·2026
Same journal

Erratum to: The landscape of complexity measures in 2D gravity.

Journal of high energy physics : JHEP·2026
Same journal

Quantum anomaly detection for collider physics.

Journal of high energy physics : JHEP·2023
Same journal

The analytic structure of the fixed charge expansion.

Journal of high energy physics : JHEP·2022
Same journal

Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim gravity.

Journal of high energy physics : JHEP·2022
Same journal

LHC lifetime frontier and visible decay searches in composite asymmetric dark matter models.

Journal of high energy physics : JHEP·2022
See all related articles

Related Experiment Video

Updated: Nov 25, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.4K

Conformal field theory complexity from Euler-Arnold equations.

Mario Flory1, Michal P Heller2

  • 1Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland.

Journal of High Energy Physics : JHEP
|December 21, 2020
PubMed
Summary
This summary is machine-generated.

This study explores quantum field theory complexity using conformal field theories in 1+1 dimensions. It introduces Euler-Arnold equations to define state and operator complexity, offering a novel approach to complex quantum systems.

Keywords:
AdS-CFT CorrespondenceConformal Field TheoryGauge-gravity correspondence

More Related Videos

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

9.8K
Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.7K

Related Experiment Videos

Last Updated: Nov 25, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.4K
Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

9.8K
Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

3.7K

Area of Science:

  • Quantum Field Theory
  • Theoretical Physics
  • Conformal Field Theory

Background:

  • Defining complexity in quantum field theory is challenging, particularly beyond simple models.
  • Existing methods often struggle with Gaussian states and operations.

Purpose of the Study:

  • To comprehensively study state and operator complexity in 1+1 dimensional conformal field theories.
  • To explore the universal sector of the energy-momentum tensor.

Main Methods:

  • Utilizing Euler-Arnold equations and their integro-differential generalizations.
  • Applying differential regularization techniques.
  • Solving integro-differential equations for Fubini-Study state complexity.

Main Results:

  • Demonstrated a well-posed optimization problem for complexity between quantum states and transformations.
  • Provided an in-depth analysis of state and operator complexity in conformal field theories.
  • Explored the geometric properties underlying quantum complexity.

Conclusions:

  • The Euler-Arnold framework offers a robust method for defining and calculating complexity in quantum field theory.
  • This work advances the understanding of complexity in non-perturbative quantum systems.