RUI: Oscillons and Casimir Forces in Classical and Quantum Field Theory

“这项奖励是根据2009年美国复苏和再投资法案（公法111-5）资助的。”场论提供了我们对自然界基本相互作用最著名的描述。在许多情况下，一个人可以通过考虑理论而取得重大进展。摄动地，从独立传播的波的集合开始。本研究项目将解决两种情况，其中这种摄动方法在根本上是失败的。第一种情况出现在考虑波形成不分散的相干团块的可能性时。虽然这类静态物体已经得到了很好的研究，但对于经历规则振荡的解（称为振荡子或呼吸子）所知甚少。这类天体在早期宇宙中尤其令人感兴趣，因为形成它们所需的巨大能量是可用的。该项目将研究粒子物理模型中振荡的存在，它们在早期宇宙中形成的速率，以及它们在产生重子形成（早期宇宙中普通物质形成的过程）所必需的非平衡条件中可能发挥的潜在作用。第二种情况出现在考虑不能用弱耦合近似的量子力学效应时。本项目将重点研究导体或强电介质中量子电磁涨落引起的卡西米尔力及其在相关理论中的类似物。在这种情况下，卡西米尔力取决于物体的几何和方向的相干性，并且与摄动得到的结果在性质上不同。最近发展的技术使计算卡西米尔力成为可能，适用于广泛的新几何形状和材料。这些技术将用于研究卡西米尔力的形状、方向和物质依赖性，并制定和试图证明控制其行为的普遍定理。类似的技术也将用于研究粒子物理标准模型中电弱弦解的卡西米尔能量。更广泛的影响如下：这项研究的技术和结果可能适用于物理学的其他分支，应用物理学和非线性动力学，以及在这项工作过程中开发的计算工具。这些工具的源代码将公开提供给其他研究人员使用。这个研究项目也将显著影响明德学院的物理教学，无论是通过直接参与的本科生，还是通过改进这项工作所产生的课程。参与其中任何一个方面的学生都将有机会发展计算物理和非线性动力学的新技能，并利用这些技能更好地理解物理学的基本概念。

"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)."Field theories provide our best known description of the fundamental interactions of Nature. In many situations, one can make significant progress by considering the theory. Perturbatively, starting from a collection of waves propagating independently.This research project will address two situations in which this perturbative approach fails in a fundamental way. The first situation arises when one considers the possibility of waves forming coherent lumps that do not disperse. While static objects of this kind have been well studied, much less is known about solutions that undergo regular oscillations, called oscillons or breathers. Such objects are especially of interest in the early universe, when the large energies needed to form them are available. This project will investigate the existence of oscillons in particle physics models, the rate at which they would have formed in the early universe, and the potential role they could play in generating the out-of-equilibrium conditions necessary for baryogenesis, the process by which ordinary matter formed in the early universe.The second situation arises when one considers quantum mechanical effects that cannot be approximated by weak coupling. This project will focus on Casimir forces induced by quantum electromagnetic fluctuations in conductors or strong dielectrics, and their analogs in related theories. In such situations the Casimir force depends on coherent properties of the geometry and orientation of the objects, and differs qualitatively from the result one would obtain perturbatively. Recently developed techniques have made it possible to calculate Casimir forces for a broad set of new geometries and materials. These techniques will be used to study shape, orientation, and material dependence of Casimir forces and to formulate and attempt to prove universal theorems governing their behavior. Similar techniques will also be used to study Casimir energies of electroweak string solutions in the Standard Model of particle physics. The broader impacts are as follows: The techniques and results of this research are potentially applicable to a wide range of other branches of physics, applied physics, and nonlinear dynamics, as are the computational tools to be developed during the course of this work. The source code for these tools will be made publicly available for use by other researchers. This research program will also significantly impact the teaching of physics at Middlebury College, both through the undergraduates directly involved and through enhancements to the curriculum that will grow out of this work. Students participating in any of these aspects will have the opportunity to develop new skills in computational physics and nonlinear dynamics, and to use these skills to better understand fundamental concepts in physics.