{"title":"Non-Archimedean Statistical Field Theory","authors":"W. A. Z'uniga-Galindo","doi":"10.1142/s0129055x22500222","DOIUrl":null,"url":null,"abstract":"We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The calculation of the correlation functions is carried out in the standard form. In the case of $\\varphi^{4}$-theories, we show the existence of systems admitting spontaneous symmetry breaking.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0129055x22500222","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The calculation of the correlation functions is carried out in the standard form. In the case of $\varphi^{4}$-theories, we show the existence of systems admitting spontaneous symmetry breaking.
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