Radiation reaction on classical and quantum electrons revisited

Abstract The dynamics of an electron interacting, in an infinite three-dimensional vacuum in an inertial system, with an electromagnetic field (an incoming radiation and the field generated by the electron) is revisited. The initial conditions are given in the infinitely remote past. Classical and quantum descriptions (with a cut-off) are considered, focusing on the radiation reaction on an electron, in the absence of positrons. In the fully classical case, the Hamiltonian description provides a new approximate derivation of the controversial contribution proportional to the time derivative of the electron acceleration. One model with non-relativistic quantum electron is analyzed. An extension to include the first relativistic correction for the quantum electron, after the Foldy-Wouthuysen transformation, is studie3d. Relativistic Quantum Electrodynamics (QED) excluding positrons is formulated in one electron subspace and numerical computations appear to justify its approximate validity for laser radiation with very high intensities, in certain ranges of radiation frequency and electron velocity (relativistic but not ultrarelativistic). For the last three models, all with quantized electromagnetic field, expectation values of the exact Lorentz force equations for the electron are derived, which include the incoming radiation and an exact radiation reaction force due to the radiated field. In the absence of incoming radiation, the radiation reaction forces vanish exactly in the three fully quantized models, as tests of consistency. With the recent advancements in multi-petawatt lasers, radiation reaction from strongly driven electrons is set to become a routinely observed phenomenon in leading laboratories, making a fundamental understanding of this process increasingly relevant.