Concepts of strong-field QED in momentum space: gauge invariance and soft-photon theorems

Usually, quantum electrodynamics acts as the prime example, when it comes to a well-understood and outstandingly precise description of elementary particle processes. However, modern laser facilities provide highly intense light with a non-trivial temporal structure, where an arbitrary number of ‘photons’ from the light source may interact with the colliding particles. In this case, the standard perturbative treatment known from quantum electrodynamics becomes cumbersome and impractical. Accordingly, there are, among others, wide theoretical investigations w.r.t. scattering processes of particles impinging these extreme light sources. This has been done by applying the strong-field quantum electrodynamics, a theory of electromagnetic interactions within coherent highly intense light treated as a classical background field. Here, the distinction between a classical background field and a quantized photon field revealed a vast amount of novel non-linear structures and non-perturbative phenomena. In this seminar, we introduce the basic concepts of strong-field QED and derive the Feynman rules for the theory in momentum space. Then, we explore their general structure and implications from fundamental principles, namely gauge invariance.