{"title":"格罗斯-涅乌模型中 RG 流的结构稳定性","authors":"J. Dimock, Cheng Yuan","doi":"10.1007/s00023-024-01427-0","DOIUrl":null,"url":null,"abstract":"<div><p>We study flow of renormalization group (RG) transformations for the massless Gross–Neveu model in a non-perturbative formulation. The model is defined on a two-dimensional Euclidean space with a finite volume. The quadratic approximation to the flow stays bounded after suitable renormalization. We show that for weak coupling this property also is true for the complete flow. As an application we prove an ultraviolet stability bound for the model. Our treatment is an application of a method of Bauerschmidt, Brydges, and Slade. The method was developed for an infrared problem and is now applied to an ultraviolet problem.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 12","pages":"5113 - 5186"},"PeriodicalIF":1.4000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Structural Stability of the RG Flow in the Gross–Neveu Model\",\"authors\":\"J. Dimock, Cheng Yuan\",\"doi\":\"10.1007/s00023-024-01427-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study flow of renormalization group (RG) transformations for the massless Gross–Neveu model in a non-perturbative formulation. The model is defined on a two-dimensional Euclidean space with a finite volume. The quadratic approximation to the flow stays bounded after suitable renormalization. We show that for weak coupling this property also is true for the complete flow. As an application we prove an ultraviolet stability bound for the model. Our treatment is an application of a method of Bauerschmidt, Brydges, and Slade. The method was developed for an infrared problem and is now applied to an ultraviolet problem.</p></div>\",\"PeriodicalId\":463,\"journal\":{\"name\":\"Annales Henri Poincaré\",\"volume\":\"25 12\",\"pages\":\"5113 - 5186\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Poincaré\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00023-024-01427-0\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s00023-024-01427-0","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Structural Stability of the RG Flow in the Gross–Neveu Model
We study flow of renormalization group (RG) transformations for the massless Gross–Neveu model in a non-perturbative formulation. The model is defined on a two-dimensional Euclidean space with a finite volume. The quadratic approximation to the flow stays bounded after suitable renormalization. We show that for weak coupling this property also is true for the complete flow. As an application we prove an ultraviolet stability bound for the model. Our treatment is an application of a method of Bauerschmidt, Brydges, and Slade. The method was developed for an infrared problem and is now applied to an ultraviolet problem.
期刊介绍:
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.