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

Limits at Infinity01:24

Limits at Infinity

85
The function that decreases as the input becomes very large provides a clear example of how mathematical functions can behave at extreme values. When the input increases continuously, the output becomes smaller and smaller, getting closer to a particular fixed value. Although the output never actually reaches this value, it moves nearer to it without limit. This behavior is a fundamental concept in understanding how functions behave as the input grows indefinitely. The graphical representation...
85
Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

3.8K
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
3.8K
Principle of Equivalence01:18

Principle of Equivalence

2.4K
According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity, for example, diving towards the Earth from an airplane, they would feel completely weightless. Similarly, a person descending in a lift may feel partially weightless. Broadly speaking, it is assumed that an object in a uniform gravitational field and an object undergoing constant acceleration in the absence of gravity are under the same...
2.4K
Gauss's Law01:07

Gauss's Law

9.1K
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
9.1K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

9.0K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
9.0K
Second Uniqueness Theorem01:16

Second Uniqueness Theorem

2.5K
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
2.5K

You might also read

Related Articles

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

Sort by
Same author

String Dualities at Order α^{'3}.

Physical review letters·2021
Same author

Duality Hierarchies and Differential Graded Lie Algebras.

Communications in mathematical physics·2021
Same author

Green-Schwarz Mechanism for String Dualities.

Physical review letters·2020
Same author

Background Independence and Duality Invariance in String Theory.

Physical review letters·2017
Same author

Exceptional form of D=11 supergravity.

Physical review letters·2014
Same author

Zwei-dreibein gravity: a two-frame-field model of 3D massive gravity.

Physical review letters·2013

Related Experiment Video

Updated: Dec 10, 2025

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.8K

Leibniz Gauge Theories and Infinity Structures.

Roberto Bonezzi1, Olaf Hohm1

  • 1Institute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, Germany.

Communications in Mathematical Physics
|August 28, 2020
PubMed
Summary

This study introduces infinity-enhanced Leibniz algebras, a novel mathematical framework for constructing gauge theories and tensor hierarchies in theoretical physics. These algebras ensure consistent structures to any level, advancing supergravity and field theory research.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

22.3K

Related Experiment Videos

Last Updated: Dec 10, 2025

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.8K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

22.3K

Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • Algebraic Structures

Background:

  • Gauge theories and tensor hierarchies are crucial in theoretical physics, particularly in gauged supergravity and exceptional field theory.
  • Existing tensor hierarchies have been limited to lower levels of complexity.
  • Leibniz(-Loday) algebras provide a foundation for formulating these theories.

Purpose of the Study:

  • To introduce a new class of algebraic structures, 'infinity-enhanced Leibniz algebras'.
  • To demonstrate how these algebras guarantee the existence of consistent tensor hierarchies to arbitrary levels.
  • To explore the relationship between these algebras and strongly homotopy Lie algebras.

Main Methods:

  • Formulation of gauge theories using Leibniz(-Loday) algebras.
  • Definition of 'infinity-enhanced Leibniz algebras'.
  • Comparison with strongly homotopy Lie algebras (SH Lie algebras).

Main Results:

  • Infinity-enhanced Leibniz algebras ensure the construction of consistent tensor hierarchies to arbitrary levels.
  • A clear mathematical structure underlying gauge theories is uncovered.
  • The association between infinity-enhanced Leibniz algebras and SH Lie algebras is established.

Conclusions:

  • The newly defined infinity-enhanced Leibniz algebras offer a powerful tool for advancing the study of gauge theories and tensor hierarchies.
  • This framework has significant implications for areas like supergravity and exceptional field theory.
  • The connection to SH Lie algebras opens avenues for further research in topological field theories.