Effective Field Theories and PDE

有效场论和偏微分方程

• 批准号: 2436109
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2436109
• 关键词: Effective; Field; Theories; PDE

In many problems in theoretical physics it is possible to make progress by exploiting a hierarchy of scales between 'heavy' and 'light' excitations. When considering excitations of the light fields, there is a well-understood process to formally remove the heavy fields from the model, leaving field equations for the light excitations which are formally given by an infinite expansion - the Effective Field Theory expansion - whose terms typically have higher and higher derivatives. This has presented a puzzle, since naively truncating such a series gives rise to pathologies. Recently progress has been made in understanding such situations rigorously. This project will bring the techniques of modern PDE analysis to bear on understanding how Effective Field Theories can arise as limits of classical PDE. In particular this will involve a detailed examination of averaging techniques for nonlinear wave equations, with applications in General Relativity and Cosmology.This falls naturally within the remit of EPSRC's Mathematical Physics and Mathematical Analysis Research Areas.

在理论物理的许多问题中，利用“重”和“轻”激发之间的尺度层次是有可能取得进展的。当考虑光场的激发时，有一个很好理解的过程可以从模型中正式删除重场，留下光激发的场方程，这些场方程由无限展开（有效场论展开）正式给出，其项通常具有越来越高的导数。这就提出了一个难题，因为天真地截断这样的序列会导致病态。最近在严格理解这种情况方面取得了进展。本项目将运用现代偏微分方程分析技术来理解有效场论是如何作为经典偏微分方程的极限而产生的。特别地，这将涉及非线性波动方程的平均技术的详细检查，以及在广义相对论和宇宙学中的应用。这自然属于EPSRC的数学物理和数学分析研究领域的职权范围。