Towards the Stochastic Quantisation of Interacting Systems of Fermions and Bosons
费米子和玻色子相互作用系统的随机量子化
基本信息
- 批准号:2602127
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:英国
- 项目类别:Studentship
- 财政年份:2021
- 资助国家:英国
- 起止时间:2021 至 无数据
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Over the past two decades, work first pioneered by Da Prato & Debussche and then expanded upon by Gubinelli, Hairer et al. has firmly established Stochastic Quantisation as a fundamental tool of Constructive Quantum Field Theory (QFT). This method involves solving so-called non-linear singular stochastic partial differential equations (SPDE). However, any potential solution to such an equation must be inherently singular, that is the functions are so ill-behaved that you cannot multiply them with themselves. This, in turn, means that we cannot a priori define what the nonlinearities are supposed to mean. Hence, the equations are ill-posed. Since the inception of QFT physicists such as Feynman, Schwinger, Weinberg et al. have continuously developed methods to deal with such singular products. We now have a bursting quiver full of methods, collectively known as "Renormalisation", at our disposal. Adapting these methods to SPDE's was the key breakthrough that allowed us to begin solving the stochastic quantisation equations, at least for Bosons. These newly enhanced methods rely, however, on the commutative nature of Bosons and thus on leveraging many techniques from probability theory and stochastic analysis.However, a major ingredient of the Standard Model of Particle Physics and Nature as a whole are Fermions, fundamentally non-commutative objects, and one is forced to realise them as objects in algebras of operators or similarly complicated structures. Thus, instead of just finding random singular functions we have to solve for random operator-valued singular functions. In particular, the procedure of renormalisation turns bounded operators, which have a very rigid and well-behaved topological structure, into unbounded operators, fickle objects which necessitate one to double-check every operation one takes for granted.In our research, we have been working towards a clean formulation of the singular non-commutative PDE's in the language of regularity structures as well as working on deriving a solution theory for specific equations describing the interaction of Bosons and Fermions that can overcome the problems outlined above. If successful this research will open up a whole new avenue for investigating physical systems that do not only contain Bosons, the force carriers of nature, but also Fermions which make up all the conventional matter in the universe. Amongst these are for example models such as Quantum Electrodynamics and Yang-Mills with ghosts.The rigorous mathematical underpinnings of QFT's, and specifically the standard model, are one of the least well-understood parts of fundamental physics and gaining more insight into their intricacies might be one of the few paths open to us to go beyond the Standard Model. Therefore, we hope that we can contribute to the knowledge of nature at its smallest scales with our research.This project falls within the EPSRC Mathematical Physics research area. The project is supervised by Dr. Ajay Chandra and Prof. Martin Hairer.
在过去的二十年里,这项工作首先由达普拉托和德布施开创,然后由古比内利、海尔等人扩展。已经牢固地确立了随机量子化作为建设性量子场论(QFT)的基本工具。这种方法涉及到求解所谓的非线性奇异随机偏微分方程(SPDE)。然而,这种方程的任何潜在解都必须是固有的奇异的,也就是说,函数表现得如此不好,以至于你不能将它们与它们自己相乘。反过来,这意味着我们不能先验地定义非线性应该意味着什么。因此,这些方程是不适定的。自Fynman、Schwinger、Weinberg等物理学家问世以来,QFT一直是物理学家研究的热点。不断发展出处理这种奇特产品的方法。我们现在有了一大堆方法,统称为“重新正规化”,可供我们使用。使这些方法适用于SPDE是关键的突破,使我们能够开始求解随机量化方程,至少对玻色子是这样。然而,这些新改进的方法依赖于玻色子的对易性质,从而利用了概率论和随机分析的许多技术。然而,粒子物理和自然的标准模型的一个主要组成部分是费米子,基本上是非对易对象,人们被迫将它们实现为算符代数或类似复杂结构中的对象。因此,我们必须求解随机算符值奇异函数,而不是仅仅寻找随机奇异函数。特别是,重整化过程将具有非常严格和良好的拓扑结构的有界算符转变为无界算符,变化无常的对象需要仔细检查每一种被认为是理所当然的操作。在我们的研究中,我们一直致力于以正则性结构的语言干净地表示奇异的非对易偏微分方程组,并致力于推导描述玻色子和费米子相互作用的特定方程的解理论,以克服上述问题。如果成功,这项研究将为研究物理系统开辟一条全新的途径,这些物理系统不仅包含玻色子,也包含组成宇宙中所有常规物质的费米子,玻色子是自然界的力载体。其中包括量子电动力学模型和带有幽灵的杨-米尔斯模型。QFT的严格数学基础,特别是标准模型,是基础物理中最不被理解的部分之一,更多地了解它们的复杂性可能是我们超越标准模型的为数不多的途径之一。因此,我们希望我们的研究能够为我们对自然的最小范围的知识做出贡献。这个项目属于EPSRC数学物理研究领域。该项目由阿贾伊·钱德拉博士和马丁·海勒教授监督。
项目成果
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其他文献
吉治仁志 他: "トランスジェニックマウスによるTIMP-1の線維化促進機序"最新医学. 55. 1781-1787 (2000)
Hitoshi Yoshiji 等:“转基因小鼠中 TIMP-1 的促纤维化机制”现代医学 55. 1781-1787 (2000)。
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LiDAR Implementations for Autonomous Vehicle Applications
- DOI:
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2021 - 期刊:
- 影响因子:0
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吉治仁志 他: "イラスト医学&サイエンスシリーズ血管の分子医学"羊土社(渋谷正史編). 125 (2000)
Hitoshi Yoshiji 等人:“血管医学与科学系列分子医学图解”Yodosha(涉谷正志编辑)125(2000)。
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Effect of manidipine hydrochloride,a calcium antagonist,on isoproterenol-induced left ventricular hypertrophy: "Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,K.,Teragaki,M.,Iwao,H.and Yoshikawa,J." Jpn Circ J. 62(1). 47-52 (1998)
钙拮抗剂盐酸马尼地平对异丙肾上腺素引起的左心室肥厚的影响:“Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,
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