S-Matrix Theory

S矩阵理论

• 批准号: SAPIN-2017-00026
• 负责人: Cachazo, Freddy
• 金额: $ 5.1万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762948
• 关键词: Matrix; Theory

Every time a new instrument, such as the telescope or the microscope, is invented that allows us to observe our Universe at larger or shorter distances than before, it has led to important changes in our understanding of nature. The most powerful “microscope” ever constructed is the Large Hadron Collider (LHC), located at CERN. It accelerates protons to nearly the speed of light, makes them collide and records to product of such collisions. Protons are not elementary particles, they are made out of quarks and gluons. The LHC collisions actually happen when quarks and gluons collide, allowing us to see deeper into the structure of fundamental particles than ever before. Our best theories of natures are put to the test by comparing their predictions to the LHC detections. These predictions were traditionally made using a technique known as Feynman diagrams. Thirty years ago, Parke and Taylor found that a very special class of these computations starts out as many-pages long only to be simplified to single-line expressions. In physics, this is an indication that some new principle or idea is hiding around the corner. For more than a decade, my research has focused on new understandings of the way quantum mechanics and Einstein's special relativity combine that extend the “Parke-Taylor miraculous phenomenon” to all kinds of interactions at the LHC. This journey has led to the discovery of connections to new areas of mathematics and to many extensions including the collision of gravitons, particles which are the force carriers of Einstein's gravity theory. A construction discovered in 2013, now known as the Cachazo-He-Yuan (CHY) formulation, indicates that this is just the tip of an iceberg of new structures that have the potential to teach us about the inner workings of spacetime itself. In this proposal, my team will continue the development of the CHY formulation, its connections to other mathematical constructions and to string theory techniques. String theory is a framework for the unification of gravity and quantum mechanics which has at its core Riemann surfaces, such as the surface of a ball, a donut, or even a pretzel. The CHY formulation also has Riemann surfaces at its core. What we know about the CHY formulation indicates that Feynman diagrams are scrambled inside the Riemann surfaces in ways that need to be understood. Since Feynman diagrams tell us a story of interactions in spacetime, our spacetime will also have to emerge from the Riemann surfaces. This indicates a connection to modern ideas in holography (as applied to Einstein gravity). Just as the CHY formulation was developed by my team at the time, S. He (a postdoctoral fellow at Perimeter Institute) and E. Yuan* (my graduate student at the University of Waterloo and Perimeter Institute), my current team of master's and PhD students is well positioned to continue playing a leadership role in this active area of research.

每当一种新的仪器，如望远镜或显微镜被发明出来，使我们能够在比以前更大或更短的距离上观察我们的宇宙时，它就会导致我们对自然的理解发生重大变化。有史以来最强大的“显微镜”是位于欧洲核子研究中心的大型强子对撞机（LHC）。它将质子加速到接近光速，使它们碰撞并记录这种碰撞的产物。质子不是基本粒子，它们由夸克和胶子组成。大型强子对撞机的碰撞实际上发生在夸克和胶子碰撞的时候，这让我们比以往任何时候都更深入地了解基本粒子的结构。我们最好的自然理论通过将它们的预测与LHC的探测进行比较来进行测试。这些预测传统上是使用一种称为费曼图的技术进行的。 30年前，帕克和泰勒发现，这些计算中有一类非常特殊的计算开始时长达数页，但最终被简化为单行表达式。在物理学中，这是一个迹象，表明一些新的原理或想法正隐藏在角落里。十多年来，我的研究一直集中在对量子力学和爱因斯坦狭义相对论联合收割机结合方式的新理解上，这些理解将“帕克-泰勒奇迹现象”扩展到LHC的各种相互作用。这一旅程导致了发现与数学新领域的联系，以及许多扩展，包括引力子的碰撞，引力子是爱因斯坦引力理论的力载体。2013年发现的一种结构，现在被称为Cachazo-He-Yuan（CHY）公式，表明这只是新结构的冰山一角，这些结构有可能教会我们时空本身的内部运作。在这个提议中，我的团队将继续发展CHY公式，它与其他数学结构和弦理论技术的联系。 弦理论是统一引力和量子力学的框架，其核心是黎曼曲面，例如球、甜甜圈甚至椒盐卷饼的表面。CHY公式也有黎曼曲面在其核心。我们对CHY公式的了解表明，费曼图在黎曼曲面中以需要理解的方式被打乱。既然费曼图告诉我们时空中相互作用的故事，我们的时空也必须从黎曼曲面中出现。这表明了与全息术的现代思想（如应用于爱因斯坦引力）的联系。正如我的团队当时开发的CHY配方一样，S。他（Perimeter Institute的博士后）和E.袁 *（我在滑铁卢大学和周边研究所的研究生），我目前的硕士和博士生团队处于有利地位，继续在这一活跃的研究领域发挥领导作用。