Investigations in Quantum Field Theory

量子场论研究

• 批准号: SAPIN-2019-00027
• 负责人: Gaiotto, Davide
• 金额: $ 5.61万
• 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=762977
• 关键词: Investigations; Quantum; Field; Theory

Quantum Field Theory is perhaps the most successful tool physicists use to describe the physical world. For example, the Standard Model, which describes in precise detail the behaviour of all known particles, is a quantum field theory. Other quantum field theories are used to describe systems of very practical interest, including superconductors and other exotic materials which lie at the core of modern and future electronic devices, such as quantum computers. The ubiquity of Quantum Field Theory in theoretical physics means that every novel idea in Quantum Field Theory reverberates through many different subjects and scientific communities, irrespectively of which community originally developed it. The study of Quantum Field Theory often involves ideas of great mathematical sophistication, which have lead to whole new perspectives on important mathematical subjects and novel connections between previously disconnected areas. This strong interdisciplinary activity at the intersection of physics and mathematics greatly benefits both subjects.   Despite being such a well-established tool, many aspects of Quantum Field Theory are still mysterious or poorly understood. Depending on the specific situation, a quantum field theory may be "weakly coupled" or "strongly coupled". Weakly coupled field theories allow us precise calculations which match in detail experimental results. They are usually considered to be well understood, though many important subtleties are still being discovered today. Strongly coupled field theories are poorly understood, and very hard to use for precise calculations. Many such theories may be still unknown and we do not have a systematic way to search for them.  These limitations in our understanding of Quantum Field Theory obstruct our progress in a variety of subjects, ranging from deep questions about the nature of the Universe to very concrete problems in material science, such as the development of superconductors able to function at room temperature.  The main objective of this proposal is to develop new computational tools and mathematical ideas to study Quantum Field Theory and to apply these tools to the solution of long standing theoretical problems in High Energy Physics, Condensed Matter Physics and Mathematics. The research activities in this program will also offer unique training opportunities to several students and young researchers, which will disseminate these tools and idea through the scientific community and beyond.  In the long term, this progress in our theoretical understanding of quantum field theories will impact our ability to tailor exotic quantum systems to practical applications, advance out understanding of the fundamental laws of the universe, and lead to deep mathematical advances. Beyond its concrete applications, reaching a full understanding of Quantum Field Theory will be one of humanity great intellectual achievements and it is worth pursuing for its own sake.

量子场论也许是物理学家用来描述物理世界的最成功的工具。例如，标准模型精确地描述了所有已知粒子的行为，是一种量子场论。其他量子场论用于描述非常实用的系统，包括超导体和其他奇异材料，这些材料是现代和未来电子设备的核心，如量子计算机。量子场论在理论物理学中的普遍性意味着量子场论中的每一个新思想都会在许多不同的学科和科学团体中产生反响，而不管最初是哪个团体开发了它。量子场论的研究通常涉及非常复杂的数学思想，这些思想导致了对重要数学学科的全新观点和以前脱节的领域之间的新颖联系。这种强大的跨学科活动在物理学和数学的交叉点极大地有利于这两个学科。 尽管量子场论是一个成熟的工具，但它的许多方面仍然是神秘的或知之甚少的。根据具体情况，量子场论可以是“弱耦合”或“强耦合”。弱耦合场理论允许我们精确的计算，详细的实验结果相匹配。人们通常认为它们已经被很好地理解了，尽管许多重要的微妙之处至今仍在被发现。强耦合场论却知之甚少，而且很难用于精确的计算。许多这样的理论可能仍然是未知的，我们没有一个系统的方法来寻找它们。我们对量子场论的理解中的这些局限性阻碍了我们在各种学科中的进步，从关于宇宙本质的深刻问题到材料科学中非常具体的问题，例如开发能够在室温下工作的超导体。该提案的主要目标是开发新的计算工具和数学思想来研究量子场理论，并将这些工具应用于解决高能物理，凝聚态物理和数学中长期存在的理论问题。该计划的研究活动还将为一些学生和年轻研究人员提供独特的培训机会，这些培训将通过科学界和其他领域传播这些工具和想法。从长远来看，我们对量子场论的理论理解的这一进展将影响我们为实际应用定制奇异量子系统的能力，推进对宇宙基本定律的理解，并带来了深刻的数学进步。除了它的具体应用之外，达到对量子场论的全面理解将是人类伟大的智力成就之一，值得为它本身而追求。