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Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)最新文献

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Introduction to the Intersection Theory for Twisted Homology and Cohomology Groups 扭曲同调与上同调群的交点理论简介
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0007
Keiji Matsumoto
{"title":"Introduction to the Intersection Theory for Twisted Homology and Cohomology Groups","authors":"Keiji Matsumoto","doi":"10.22323/1.383.0007","DOIUrl":"https://doi.org/10.22323/1.383.0007","url":null,"abstract":"We give an introduction to the intersection theory for twisted homology and cohomology groups associated with Euler type integrals of hypergeometric functions. We introuduce twisted homology and cohomology groups motivated by Twisted Stokes’ Theorem, and give their dimension formulas. We define an intersection form between twisted homology groups and that between twisted cohomology groups, and explain how to compute them. These intersection forms are compatible with the natural pairing between the twisted homology and cohomology groups. This compatibility yields a twisted period relation, which relates intersection numbers and period integrals regarded as some kinds of hypergeometric functions. In Appendix, we show that Elliott’s identity can be obtained from the twisted period relation.","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134477502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Product of Hessians and Discriminant of Critical Points of Level Function for Hypergeometric Integrals 超几何积分中层次函数临界点的判别与Hessians积
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0009
K. Aomoto, Masahiko Ito
{"title":"Product of Hessians and Discriminant of Critical Points of Level Function for Hypergeometric Integrals","authors":"K. Aomoto, Masahiko Ito","doi":"10.22323/1.383.0009","DOIUrl":"https://doi.org/10.22323/1.383.0009","url":null,"abstract":"We give in two examples (hyperplane arrangement and circle arrangement) a relation between the product of the Hessians of a level function associated with hypergeometric integrals and discriminant attached to them. We also express the product of values of prime factors of integrand at critical points by the use of basic invariants attached to each arrangement. Our main goal is to give a criterion in terms of the product of Hessians for that all critical points are different from each other.","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"245 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121121499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Schwarz maps for the hypergeometric function 超几何函数的Schwarz映射
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0011
Masaaki Yoshida
{"title":"Schwarz maps for the hypergeometric function","authors":"Masaaki Yoshida","doi":"10.22323/1.383.0011","DOIUrl":"https://doi.org/10.22323/1.383.0011","url":null,"abstract":"","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127148062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximal Cuts and Wick Rotations 最大切割和灯芯旋转
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0002
E. Remiddi
{"title":"Maximal Cuts and Wick Rotations","authors":"E. Remiddi","doi":"10.22323/1.383.0002","DOIUrl":"https://doi.org/10.22323/1.383.0002","url":null,"abstract":"","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"149 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133000094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Connection formulas related with Appell's hypergeometric function $F_1$ 与阿佩尔超几何函数$F_1$有关的连接公式
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0010
K. Mimachi
{"title":"Connection formulas related with Appell's hypergeometric function $F_1$","authors":"K. Mimachi","doi":"10.22323/1.383.0010","DOIUrl":"https://doi.org/10.22323/1.383.0010","url":null,"abstract":"","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126007550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Application of Intersection Theory to Feynman Integrals: the multivariate case 交点理论在费曼积分中的应用:多元情况
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0019
M. K. Mandal, Federico Gasparotto
{"title":"On the Application of Intersection Theory to Feynman Integrals: the multivariate case","authors":"M. K. Mandal, Federico Gasparotto","doi":"10.22323/1.383.0019","DOIUrl":"https://doi.org/10.22323/1.383.0019","url":null,"abstract":"","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128119232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Appell-Lauricella's hypergeometric functions and intersection theory aap - lauricella的超几何函数与交点理论
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0008
Y. Goto
{"title":"Appell-Lauricella's hypergeometric functions and intersection theory","authors":"Y. Goto","doi":"10.22323/1.383.0008","DOIUrl":"https://doi.org/10.22323/1.383.0008","url":null,"abstract":"","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121058500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Intersection theory, characteristic classes, and algebro-geometric Feynman rules 交集理论，特征类，和代数几何费曼规则
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0012
P. Aluffi, M. Marcolli
{"title":"Intersection theory, characteristic classes, and algebro-geometric Feynman rules","authors":"P. Aluffi, M. Marcolli","doi":"10.22323/1.383.0012","DOIUrl":"https://doi.org/10.22323/1.383.0012","url":null,"abstract":"We review the basic definitions in Fulton-MacPherson Intersection Theory and discuss a theory of ‘characteristic classes’ for arbitrary algebraic varieties, based on this intersection theory. We also discuss a class of graph invariants motivated by amplitude computations in quantum field theory. These ‘abstract Feynman rules’ are obtained by studying suitable invariants of hypersurfaces defined by the Kirchhoff-Tutte-Symanzik polynomials of graphs. We review a ‘motivic’ version of these abstract Feynman rules, and describe a counterpart obtained by intersection-theoretic techniques.","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129059542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From Diagrammar to Diagrammalgebra
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0015
P. Mastrolia
{"title":"From Diagrammar to Diagrammalgebra","authors":"P. Mastrolia","doi":"10.22323/1.383.0015","DOIUrl":"https://doi.org/10.22323/1.383.0015","url":null,"abstract":"","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122409392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Four-loop master integrals and hypergeometric functions 四环主积分和超几何函数
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019) Pub Date : 2022-02-15 DOI: 10.22323/1.383.0023
S. Laporta
{"title":"Four-loop master integrals and hypergeometric functions","authors":"S. Laporta","doi":"10.22323/1.383.0023","DOIUrl":"https://doi.org/10.22323/1.383.0023","url":null,"abstract":"We recall the analytical result of the 4-loop QED contribution to the electron g-2 and slope, which contain elliptic constants. We describe the relations between four elliptic constants which have 4F3 hypergeometric expressions. In particular we consider a quadratic relation found by Broadhurst and Mellit, and, by introducing a free parameter, we generalize it to a new quadratic relation between values of the hypergeometric 4F3.","PeriodicalId":173323,"journal":{"name":"Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123035444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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