Fresh perspectives for QED in intense backgrounds: first quantised techniques in strong field QED

量子电动力学（QED）控制着光和物质相互作用的方式，它是我们最成熟的基础物理学理论。与其他物理问题一样，QED中的问题通常可以用一种称为微扰理论的近似方案来解决。在这里，人们在一个适当的小膨胀参数中进行低阶计算，在QED中，这个参数是众所周知的与电荷的平方成正比的“精细结构常数”。在微扰理论中采用顺序高阶可以提供更高精度的结果，但现在需要在非常高阶甚至所有阶的制度中取得进展，以获得有意义的理论见解并做出足够精确的实验预测。这种情况发生在激光与物质的相互作用中，相关的高阶计算是非常具有挑战性的。现代激光设备产生具有非常高光子密度的强光脉冲，通常将相当于太阳发射的总光聚焦到针的头部。激光光子与物质的相互作用相干地增加，所以这些大量的入射光子意味着激光与物质的耦合得到了有效的增强，从精细结构常数到所谓的“无量纲强度参数”。这个参数在目前的设施中很容易超过单位-未来的实验将达到10到100的值-这显然需要非扰动处理。幸运的是，这种激光-物质相互作用的方法是通过“毛茸茸的膨胀”实现的，可以被认为是一种改进的微扰理论，它包括激光光子的影响，因此可以解释无量纲强度参数的大值。这基本上是过去、现在和将来所有强激光实验的理论支柱。然而，Ritus-Narozhny猜想指出，当我们达到更高的强度时，即使在Furry膨胀中通常被忽略的量子“环路”效应也会被激光强度增强，以至于所有的环路顺序都需要被考虑在内——实际上，Furry膨胀会崩溃，让我们失去关键的理论工具。不仅仅是一个技术或数学问题，Ritus-Narozhny猜想的有趣含义是，QED的高强度状态是完全非微扰的，或者说是“强耦合的”，因此标准近似方案无法实现。因此，我们目前无法对该状态的物理特性给出任何具体的预测，也无法回答关于QED极高强度行为的其他问题，因为在强场中进行非微扰计算是非常困难的，至少使用社区采用的标准技术是如此。因此，了解高强度状态的物理特性，并识别新效应的“确凿证据”信号，以便在未来的实验中寻找，是一项需要新方法的挑战。世界线技术在量子场论中因其计算效率而受到高度重视，但它们在SFQED中的用途直到最近才被注意到，而且在英国采用这种方法的情况非常有限。本项目将发展电磁背景下研究量子傅立叶变换所需的世界级方法，并将其应用于强场问题。特别令人感兴趣的是，在世界范围的形式主义中，为所有类的高阶过程导出“主公式”的能力；这是目前在强场中所缺乏的，但如果我们要理解高强度状态的物理学，高阶效应变得重要，这是必需的。该项目将支持在世界范围内向英国和欧盟SFQED社区传播专业知识，并将为强激光场中物质的微扰和非微扰方面提供新的启示。

Quantum electrodynamics (QED) governs the way that light and matter interact and it is our best-tested theory of fundamental physics. Problems in QED can very often be approached, as with other physics problems, in an approximate scheme called perturbation theory. Here one performs calculations to low order in a suitably small expansion parameter, which in QED is the well-known "fine structure constant" proportional to the square of the electric charge. Going to sequentially higher orders in perturbation theory may provide higher precision results, but advances are now required in regimes of very high orders, or even all orders, to obtain meaningful theoretical insight and make sufficiently precise experimental predictions. Such a situation occurs in laser-matter interactions, and the associated higher order calculations are prohibitively challenging. Modern laser facilities create pulses of intense light with very high photon density, often focussing the equivalent of the total light emitted by the sun onto the head of a pin. The interaction of laser photons with matter adds coherently, so these great numbers of incident photons imply that the laser-matter coupling effectively becomes enhanced, from the fine-structure constant to the so-called "dimensionless intensity parameter." This parameter easily exceeds unity at current facilities - and future experiments will reach values of 10 to 100 - which clearly demands a non-perturbative treatment. Fortunately, such an approach to laser-matter interactions is made possible by the "Furry expansion," can be thought of as an improved perturbation theory that includes the effects of laser photons, thereby accounting for large values of the dimensionless intensity parameter. This is the theoretical backbone of essentially all previous, current, and future intense laser experiments.However, the Ritus-Narozhny conjecture states that as we go ever higher intensities, quantum "loop" effects, which are typically neglected even in the Furry expansion, also become enhanced by laser intensity, to such an extent that all loop orders need to be accounted for -- in effect, the Furry expansion breaks down, leaving us without our key theoretical tool. More than simply a technical or mathematical problem, the intriguing implication of the Ritus-Narozhny conjecture is that the high-intensity regime of QED is fully non-perturbative, or "strongly coupled" and therefore inaccessible to standard approximation schemes. We are therefore currently unable to give any concrete predictions for the physics of this regime, or to answer other questions on the very high intensity behaviour of QED, because non-perturbative calculations in strong fields are prohibitively difficult, at least with the standard techniques employed by the community. Understanding the physics of the high-intensity regime, and identifying "smoking gun" signals of new effects which can be searched for at future experiments, is therefore a challenge which requires new methods.Worldline techniques are highly valued in quantum field theory for their calculational efficiency, yet their usefulness in SFQED has only recently been noticed, and the take-up of such methods in the UK has been very limited. This project will develop the worldline methods required for studying QFT in electromagnetic backgrounds and apply them to strong field problems. Of particular interest is the ability, in the worldline formalism, to derive "master formulae" for whole classes of higher-order processes; this is something which is currently lacking in strong fields, but which is required if we are to understand the physics of the high-intensity regime where higher order effects become important. The project will support national diffusion of expertise in the worldline approach, to the UK and EU SFQED community, and will shed new light on perturbative and non-perturbative aspects of matter in intense laser fields.