RUI: Solitons and Quantum Field Theory

RUI：孤子和量子场论

• 批准号: 2112781
• 负责人: Andrew Royston
• 金额: $ 13.5万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-15 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2112781&HistoricalAwards=false
• 关键词: RUI; Solitons; Quantum; Field; Theory

This award funds the research activities of Professor Andy Royston at Penn State Fayette, The Eberly Campus.The concept of a "field" is central to physics and everyday life. Fields (such as electric fields and magnetic fields) exist throughout space and enable the transmission of forces like gravity, electricity, and magnetism. Light and radio waves, for example, are ripples in an electromagnetic field. "Quantum field theory" is the mathematical framework theoretical physicists use to describe fundamental particles as discrete ripples in a field. In his research, Professor Royston aims to apply novel approaches centered on the use of objects called "solitons" to address two difficult and long-standing questions in quantum field theory. A soliton is a special type of particle that can exist when fields self-interact; one can imagine a soliton as a knot of tangled-up field. By studying the mathematical description of solitons interacting with each other and with ordinary particles, Professor Royston aims to understand mechanisms for certain particle creation and decay processes beyond the reach of traditional computational methods. Research on the mathematical structure of quantum field theory thus advances the national interest by promoting the progress of science at its most foundational level. This project will also have significant broader impacts. Professor Royston will involve undergraduates in his research, exposing them to basic science and teaching them practical skills such as computer coding and numerical analysis that will benefit them in STEM careers.More technically, the first question Professor Royston will address is that of determining the leading contribution of virtual soliton-antisoliton pairs to processes involving perturbative particles. Through crossing symmetry in quantum field theory, such contributions are related to a soliton that emits or absorbs a high energy particle resulting in a large momentum transfer of order the mass of the soliton. Professor Royston will combine semiclassical techniques with a new tool --- the forced soliton equation --- to analyze this process. The forced soliton equation, discovered by Professor Royston and collaborators in 2020, is a wavelike equation that describes a soliton being driven along an arbitrarily specifiable trajectory. The second question Professor Royston will address concerns "wall-crossing" phenomena for soliton bound-state spectra in certain supersymmetric gauge theories, and focuses on the manner in which wall-crossing can be understood from the semiclassical perspective of soliton field configurations and moduli spaces. In recent work, Professor Royston has noted a close connection between wall-crossing phenomena for magnetic monopoles and a construction in mathematics that aims to provide a compactification of monopole moduli space as a manifold with corners. Professor Royston, working in collaboration with a leading mathematician, aims to give a complete description of wall-crossing by analyzing the jumping behavior of zero-energy bound states in a certain quantum mechanics on monopole moduli space.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项资助了宾夕法尼亚州立大学费耶特分校Eberly校区的Andy Royston教授的研究活动。“场”的概念是物理学和日常生活的核心。 场（如电场和磁场）存在于整个空间，并使重力，电力和磁力等力的传输成为可能。 例如，光和无线电波是电磁场中的涟漪。 “量子场论”是理论物理学家用来描述基本粒子作为场中离散涟漪的数学框架。 在他的研究中，罗伊斯顿教授的目标是应用新的方法，集中在使用被称为“孤子”的对象，以解决量子场论中两个困难和长期存在的问题。 孤立子是一种特殊类型的粒子，当场相互作用时可以存在;人们可以将孤立子想象为纠缠场的结。 通过研究孤子相互作用和与普通粒子相互作用的数学描述，罗伊斯顿教授旨在了解传统计算方法无法达到的某些粒子创建和衰变过程的机制。 因此，对量子场论数学结构的研究通过在最基础的层面上促进科学的进步来促进国家利益。 该项目还将产生广泛的影响。 罗伊斯顿教授将让本科生参与他的研究，让他们接触基础科学，并教授他们计算机编码和数值分析等实用技能，这将使他们在STEM职业生涯中受益。从技术上讲，罗伊斯顿教授将解决的第一个问题是确定虚拟孤立子-反孤立子对对涉及微扰粒子的过程的主要贡献。 通过量子场论中的交叉对称性，这种贡献与发射或吸收高能粒子的孤子有关，导致孤子质量级的大动量转移。 Royston教授将把联合收割机半经典技术与一种新的工具--强迫孤子方程--结合起来分析这一过程。 Royston教授及其合作者在2020年发现的强迫孤子方程是一个波动方程，描述了孤子沿着沿着任意指定的轨迹被驱动。 第二个问题教授罗伊斯顿将解决关注的“跨壁”现象的孤子束缚态谱在某些超对称规范理论，并侧重于在其中跨壁可以理解的方式从半经典的角度孤子场配置和模空间。 在最近的工作中，Royston教授注意到磁单极子的跨壁现象与数学中的一种构造之间的密切联系，该构造旨在提供一种紧化的模空间作为一种带角的流形。 Royston教授与一位著名数学家合作，旨在通过分析量子力学中的零能束缚态在模空间上的跳跃行为，对穿墙进行完整的描述。该奖项反映了NSF的法定使命，通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。