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Four Lectures on Euler Integrals

by Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, Simon Telen

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Sebastian Mizera
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-09-06
Date submitted: 2023-06-29 02:56
Submitted by: Mizera, Sebastian
Submitted to: SciPost Physics Lecture Notes
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.

Published as SciPost Phys. Lect. Notes 75 (2023)

Submission & Refereeing History

Reports on this Submission

Anonymous Report 2 on 2023-8-17 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2306.13578v1, delivered 2023-08-17, doi: 10.21468/SciPost.Report.7667


This is a manuscript which perfectly fits into SciPost Physics Lecture Notes.
The manuscript discusses certain integrals, introduced as generalized Euler integrals
by Gelfand, Kapranov and Zelevinsky. In the manuscript they are simply called Euler integrals.
The importance for physics lies in the fact that they are closely related to integrals
appearing in string amplitudes and Feynman integrals.
The authors make this connection very clear by explicit examples and also
address the subtleties in the last section.
The authors summarise in less than 50 pages the main results from mathematics on Euler integrals.
They also provide short code snippets to do actual calculations.
This makes the manuscript a very valuable resource for physicists to get into this subject.

The manuscript clearly meets the criteria for SciPost Physics Lecture Notes:
It covers an important subject of current interest, and it presents material, which otherwise can only be digged out
by reading through numerous original research articles and books.
I strongly recommend the manuscript for publication in SciPost Physics Lecture Notes.

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Anonymous Report 1 on 2023-8-7 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2306.13578v1, delivered 2023-08-07, doi: 10.21468/SciPost.Report.7618


This is an excellent paper. Details in the pdf attachment


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