RUI: Scattering Approach to Quantum Fluctuations: Casimir Forces, Curved Spacetime, and Solitons

该RUI奖资助了佛蒙特州明德学院Noah Graham教授的研究活动。我们通过波的反射、传输和吸收来了解我们的世界，从蓝天散射的光到穿过地球的地震波。因此，分析波散射的数学和计算工具在我们的科学和技术基础设施中起着至关重要的作用。这项研究将发展和扩展散射理论技术，并应用它们来回答有关基本物理定律的问题，并分析和设计纳米技术中微机电系统的实验。由于散射理论在科学和工程领域发挥着重要作用，本研究为本科生在科学、技术、工程和数学（STEM）领域规划职业生涯提供了有价值的培训。因此，该项目将通过在基础和应用研究方面取得进展以及建立下一代科学家和工程师的核心技术能力来促进关键的国家优先事项。通过教育和推广，这个项目的影响将超越直接参与的学生，扩展到更广泛的大学和当地社区。更具体地说，本研究将发展解析散射理论中变相方法的扩展，然后使用这些技术来解决量子场论中的微妙问题。这些应用包括计算粒子物理模型中磁单极子的能量和电荷的量子修正，分析弯曲时空中量子涨落的影响及其对广义相对论和量子引力的影响，以及精确确定与纳米技术相关的系统中的卡西米尔力。因为它将量子场论中的问题简化为更简单和更熟悉的波散射特性，这种方法为从事这项研究的本科生提供了重要的机会，以建立广泛适用的科学和技术技能，以及将这项研究与物理课程相结合的教学机会。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This RUI award funds the research activities of Professor Noah Graham at Middlebury College in Middlebury, Vermont. We learn about our world via the reflection, transmission, and absorption of waves, from the light scattered by a blue sky to the rumble of seismic waves through the earth. As a result, the mathematical and computational tools for analyzing wave scattering play an essential role in our scientific and technological infrastructure. This research will develop and extend techniques of scattering theory and apply them both to answer questions about fundamental laws of physics and to analyze and design experiments studying microelectromechanical systems in nanotechnology. Because of the fundamental role scattering theory plays across science and engineering, this research is accessible to and provides valuable training for undergraduate students planning careers in a wide range of Science, Technology, Engineering, and Mathematics (STEM) fields. The project will thus promote key national priorities through both advances in fundamental and applied research and in building the core technical capabilities of the next generation of scientists and engineers. Through education and outreach, the impact of this project will extend beyond the students directly involved to the broader college and local community as well.More specifically, this research will develop extensions of the variable phase method in analytic scattering theory and then use these techniques to address subtle questions in quantum field theory. These applications include computations of quantum corrections to the energies and charges of magnetic monopoles in models of particle physics, analysis of the effects of quantum fluctuations in curved spacetime and their consequences for general relativity and quantum gravity, and precise determination of Casimir forces in systems relevant to nanotechnology. Because it reduces problems in quantum field theory to the simpler and more familiar properties of wave scattering, this approach offers significant opportunities for undergraduate students working on this research to build broadly applicable scientific and technical skills, as well as opportunities for pedagogical integration of this research with the physics curriculum.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.