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.
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