{"title":"标量场模型的临界行为与稳定性问题","authors":"R. Vladimir","doi":"10.17352/amp.000061","DOIUrl":null,"url":null,"abstract":"As shown in the works [1-3], the asymptotic behavior of the propagator in the Euclidean region of momenta for the model of a complex scalar field φ and a real scalar field χ with the interaction drastically changes depending on the value of the coupling constant. For small values of the coupling, the propagator of the field φ behaves asymptotically as free, while in the strong-coupling region the propagator in the deep Euclidean region tends to be a constant. In this paper, the influence of the vacuum stability problem of this model on this critical behavior is investigated. It is shown that within the framework of the approximations used, the addition of a stabilizing term of type to the Lagrangian leads to a renormalization of the mass and does not change the main effect of changing the ultraviolet behavior of the propagator. PACS number: 11.10.Jj.","PeriodicalId":430514,"journal":{"name":"Annals of Mathematics and Physics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Critical behavior and stability problem in a scalar field model\",\"authors\":\"R. Vladimir\",\"doi\":\"10.17352/amp.000061\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"As shown in the works [1-3], the asymptotic behavior of the propagator in the Euclidean region of momenta for the model of a complex scalar field φ and a real scalar field χ with the interaction drastically changes depending on the value of the coupling constant. For small values of the coupling, the propagator of the field φ behaves asymptotically as free, while in the strong-coupling region the propagator in the deep Euclidean region tends to be a constant. In this paper, the influence of the vacuum stability problem of this model on this critical behavior is investigated. It is shown that within the framework of the approximations used, the addition of a stabilizing term of type to the Lagrangian leads to a renormalization of the mass and does not change the main effect of changing the ultraviolet behavior of the propagator. PACS number: 11.10.Jj.\",\"PeriodicalId\":430514,\"journal\":{\"name\":\"Annals of Mathematics and Physics\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Mathematics and Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17352/amp.000061\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17352/amp.000061","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Critical behavior and stability problem in a scalar field model
As shown in the works [1-3], the asymptotic behavior of the propagator in the Euclidean region of momenta for the model of a complex scalar field φ and a real scalar field χ with the interaction drastically changes depending on the value of the coupling constant. For small values of the coupling, the propagator of the field φ behaves asymptotically as free, while in the strong-coupling region the propagator in the deep Euclidean region tends to be a constant. In this paper, the influence of the vacuum stability problem of this model on this critical behavior is investigated. It is shown that within the framework of the approximations used, the addition of a stabilizing term of type to the Lagrangian leads to a renormalization of the mass and does not change the main effect of changing the ultraviolet behavior of the propagator. PACS number: 11.10.Jj.