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

Line, Surface, and Volume Integrals01:15

Line, Surface, and Volume Integrals

A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...
Linear Differential Equations01:27

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...
Fundamental Theorem of Calculus I01:23

Fundamental Theorem of Calculus I

Solving problems involving definite integrals requires a systematic approach that ensures clarity and efficiency. The first step is understanding the problem by identifying the calculated quantity, whether it involves accumulation, area, or a physical concept like force or probability. It is essential to recognize given conditions, such as the range of integration and any constraints that may affect the solution. Before computing, key properties of definite integrals should be analyzed to...
Introduction to Differential Equations01:20

Introduction to Differential Equations

A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Geometric Sequences01:30

Geometric Sequences

In systems where values diminish by a constant proportion at each stage, the resulting sequence follows a geometric structure. Each new value in the sequence is obtained by applying a fixed multiplier to the preceding term. This regular, proportional decline type is often used to represent processes involving gradual loss, such as energy dissipation or reduction in amplitude over time.When analyzing the total effect of such a process across unlimited iterations, the series of values is referred...

You might also read

Related Articles

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

Sort by
Same author

Immune-metabolic trajectories delineate subgroups in paediatric long COVID.

Nature communications·2026
Same author

The influence of the color design of auditoriums on room acoustic impression.

The Journal of the Acoustical Society of America·2026
Same author

Complete Function Space for Planar Two-Loop Six-Particle Scattering Amplitudes.

Physical review letters·2025
Same author

A measuring instrument for the perceptual dimensions of road traffic noisea).

The Journal of the Acoustical Society of America·2025
Same author

Identifying periphery biomarkers of first-episode drug-naïve patients with schizophrenia using machine-learning-based strategies.

Progress in neuro-psychopharmacology & biological psychiatry·2025
Same author

Animal Models for Long COVID: Current Advances, Limitations, and Future Directions.

Journal of medical virology·2025

Related Experiment Video

Updated: Jul 8, 2026

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

Geometric Bookkeeping Guide to Feynman Integral Reduction and ϵ-Factorized Differential Equations.

Iris Bree1, Federico Gasparotto2, Antonela Matijašić1

  • 1Johannes Gutenberg-Universität Mainz, PRISMA Cluster of Excellence, Institut für Physik, D-55099 Mainz, Germany.

Physical Review Letters
|July 7, 2026
PubMed
Summary
This summary is machine-generated.

We developed an efficient algorithm for Feynman integral reduction and epsilon-factorized differential equations. This method simplifies calculations by trivializing epsilon dependence and directly yielding master integrals.

Related Experiment Videos

Last Updated: Jul 8, 2026

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

Area of Science:

  • Quantum Field Theory
  • High-Energy Physics
  • Mathematical Physics

Background:

  • Feynman integral reduction is crucial for calculating scattering amplitudes in quantum field theory.
  • Existing methods for Feynman integral reduction can be computationally intensive.
  • Epsilon-factorized differential equations simplify the analysis of divergent integrals.

Purpose of the Study:

  • To present a systematic and efficient algorithm for Feynman integral reduction.
  • To obtain epsilon-factorized differential equations for Feynman integrals.
  • To improve the efficiency of the Laporta algorithm.

Main Methods:

  • Trivializing epsilon dependence in integration-by-parts identities using specific prefactors.
  • Employing a specific order relation in the Laporta algorithm to directly obtain master integrals.
  • Proving the transformation of differential equations to an epsilon-factorized form.

Main Results:

  • A novel algorithm for Feynman integral reduction and epsilon-factorized differential equations.
  • Demonstration of trivializing epsilon dependence in integration-by-parts identities.
  • Direct derivation of master integrals with differential equations in Laurent polynomial form.

Conclusions:

  • The proposed method provides a systematic approach to obtain epsilon-factorized differential equations.
  • The improvements significantly enhance the efficiency of Feynman integral reduction.
  • This work offers a powerful tool for theoretical physics calculations.