Tests of classical and quantum electrodynamics with intense laser fields

Classical electrodynamics (CED) and quantum electrodynamics (QED) are well established physical theories and their predictions have been confirmed experimentally in various regimes and with extremely high accuracy. However, there are still areas of CED and of QED that deserve theoretical and experimental investigation, especially when physical processes occur in the presence of strong background electromagnetic fields, i.e., of the order of the so-called critical field of QED. In the presence of electromagnetic fields of such a high strength even the vacuum becomes unstable and electron-positron pair production spontaneously occurs. In view of the increasingly stronger available laser fields it is becoming feasible to employ them to test CED and QED under the extreme conditions supplied by intense fields [1]. After a broad introduction on CED and QED, I will describe different regimes of laser-matter interaction at ultra-high laser intensities and introduce present and upcoming experimental efforts to test the two theories under such extreme conditions. As a prominent theoretical example of open problems which can be addressed also experimentally, I will focus on the socalled ‘radiation reaction’ problem: classically, when a charged particle is accelerated by an external field, it emits radiation and this emission alters the motion of the charge itself. The problem of finding a self-consistent equation of motion in the realm of CED, which takes into account the electromagnetic energy-momentum loss of the electron, has resulted in unphysical equations, which have raised a long-standing, still open debate on the subject already at a classical level. Finally, the quantum origin of radiation reaction and other open issues in strongfield QED physics like the interaction among photons in vacuum, which is forbidden classically, will be discussed. [1] A. Di Piazza, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, Rev. Mod. Phys. 84, 1177 (2012).