{"title":"GKZ超几何系统中的Feynman积分关系","authors":"Henrik J. Munch","doi":"10.22323/1.416.0042","DOIUrl":null,"url":null,"abstract":"We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic scales. Utilizing the GKZ system and its relation to $D$-module theory, we propose a novel method for obtaining differential equations for master integrals. This note is based on the longer manuscript arXiv:2204.12983.","PeriodicalId":151433,"journal":{"name":"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)","volume":"117 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Feynman Integral Relations from GKZ Hypergeometric Systems\",\"authors\":\"Henrik J. Munch\",\"doi\":\"10.22323/1.416.0042\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic scales. Utilizing the GKZ system and its relation to $D$-module theory, we propose a novel method for obtaining differential equations for master integrals. This note is based on the longer manuscript arXiv:2204.12983.\",\"PeriodicalId\":151433,\"journal\":{\"name\":\"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)\",\"volume\":\"117 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22323/1.416.0042\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22323/1.416.0042","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Feynman Integral Relations from GKZ Hypergeometric Systems
We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic scales. Utilizing the GKZ system and its relation to $D$-module theory, we propose a novel method for obtaining differential equations for master integrals. This note is based on the longer manuscript arXiv:2204.12983.
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