{"title":"A Dynamical Yukawa\\(_{2}\\) Model","authors":"Ajay Chandra, Martin Hairer, Martin Peev","doi":"10.1007/s00220-024-05147-8","DOIUrl":null,"url":null,"abstract":"<div><p>We prove local (in space and time) well-posedness for a mildly regularised version of the stochastic quantisation of the <span>\\(\\hbox {Yukawa}_{{2}}\\)</span> Euclidean field theory with a self-interacting boson. Our regularised dynamic is still singular but avoids non-local divergences, allowing us to use a version of the Da Prato–Debussche argument (Da Prato and Debussche in Ann Probab 31(4):1900–1916, 2003. https://doi.org/10.1214/aop/1068646370). This model is a test case for a non-commutative probability framework for formulating the kind of singular SPDEs arising in the stochastic quantisation of field theories mixing both bosons and fermions.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05147-8.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05147-8","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We prove local (in space and time) well-posedness for a mildly regularised version of the stochastic quantisation of the \(\hbox {Yukawa}_{{2}}\) Euclidean field theory with a self-interacting boson. Our regularised dynamic is still singular but avoids non-local divergences, allowing us to use a version of the Da Prato–Debussche argument (Da Prato and Debussche in Ann Probab 31(4):1900–1916, 2003. https://doi.org/10.1214/aop/1068646370). This model is a test case for a non-commutative probability framework for formulating the kind of singular SPDEs arising in the stochastic quantisation of field theories mixing both bosons and fermions.
我们证明了具有自相互作用玻色子的\(\hbox {Yukawa}_{{2}}\)欧几里得场论的随机量子化的温和正则版本的局部（在空间和时间上）适定性。我们的正则化动态仍然是奇异的，但避免了非局部发散，允许我们使用一个版本的Da Prato - Debussche论证（Da Prato and Debussche in Ann Probab 31(4): 1900-1916, 2003）。https://doi.org/10.1214/aop/1068646370)。该模型是一个非交换概率框架的测试案例，用于在混合玻色子和费米子的场论的随机量子化中形成奇异spde。
期刊介绍：
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
