On the High-Energy Behaviour of Stong-Field QED in an Intense Plane Wave

We study the high-energy behaviour of QED in a strong plane wave electromagnetic background field generated by a laser pulse. Earlier calculations in this field hinted that under this circumstances the coupling constant of QED may increase with the 2/3-power of the energy scale for high energies and not logarithmic like in normal vacuum QED. Nevertheless, this calculations were performed in the limit of low laser frequencies or constant-crossed-fields. We show in this work that this limit does not commute with the high-energy limit and thus the power-law scaling just pertains to the constant-crossed field limit. Further we calculate the asymptotic expression of the polarization and mass operator in a strong laser pulse in the limit of high energetic photons and electrons, respectively, and obtain that they scale double logarithmic with the energy scale. Using this we show that also the probability for non-linear Breit-Wheeler pair production and for non-linear Compton scattering scales logarithmic with the energy like in vacuum QED

QED radiative corrections in a strong plane-wave background field

In this thesis radiative corrections to the probabilities of two basic processes in Quantum Electrodynamics (QED) in the presence of a strong electromagnetic plane wave background field are investigated. The considered two processes are nonlinear Compton scattering (the emission of a single photon by an electron) and nonlinear Breit-Wheeler pair production (the decay of a photon into an electron-positron pair). Taking radiative corrections into account, the electron, positron, and photon states inside a plane wave are not stable, but "decay" in the sense that electrons and positrons emit photons and photons decay into electron-positron pairs. Employing these states, the probabilities for nonlinear Compton scattering and nonlinear Breit-Wheeler pair production are derived analytically within the local constant field approximation. The particles states decay leads to the appearance of an exponential damping term in those probabilities, limiting them to values below unity even for plane wave pulses with large phase duration and intensity. Afterwards, leading order corrections in the fine-structure constant $\alpha$ to the probability of nonlinear Compton scattering, stemming from the self-interaction of the electron inside a plane wave, are investigated separately. It is shown that those corrections are included in the previously obtained probability within the same approximations

High-energy behavior of strong-field QED in an intense plane wave

Analytical calculations of radiative corrections in strong-field QED have hinted that in the presence of an intense plane wave the effective coupling of the theory in the high-energy sector may increase as the $(2/3)$-power of the energy scale. These findings have raised the question of their compatibility with the corresponding logarithmic increase of radiative corrections in QED in vacuum. However, all these analytical results in strong-field QED have been obtained within the limiting case of a background constant crossed field. Starting from the polarization operator and the mass operator in a general plane wave, we show that the constant-crossed-field limit and the high-energy limit do not commute with each other and identify the physical parameter discriminating between the two alternative limits orders. As a result, we find that the power-law scaling at asymptotically large energy scales pertains strictly speaking only to the case of a constant crossed background field, whereas high-energy radiative corrections in a general plane wave depend logarithmically on the energy scale as in vacuum. However, we also confirm the possibility of testing the ``power-law'' regime experimentally by means of realistic setups involving, e.g., high-power lasers or high-density electron-positron bunches.Comment: 29 pages, 4 figure

First-order strong-field QED processes including the damping of particles states

Volkov states are exact solutions of the Dirac equation in the presence of an arbitrary plane wave. Volkov states, as well as free photon states, are not stable in the presence of the background plane-wave field but "decay" as electrons/positrons can emit photons and photons can transform into electron-positron pairs. By using the solutions of the corresponding Schwinger-Dyson equations within the locally-constant field approximation, we compute the probabilities of nonlinear single Compton scattering and nonlinear Breit-Wheeler pair production by including the effects of the decay of electron, positron, and photon states. As a result, we find that the probabilities of these processes can be expressed as the integral over the light-cone time of the known probabilities valid for stable states per unit of light-cone time times a light-cone time-dependent exponential damping function for each interacting particle. The exponential function for an incoming (outgoing) either electron/positron or photon at each light-cone time corresponds to the total probability that either the electron/positron emits a photon via nonlinear Compton scattering or the photon transforms into an electron-positron pair via nonlinear Breit-Wheeler pair production until that light-cone time (from that light-cone time on). It is interesting that the exponential damping terms depend not only on the particles momentum but also on their spin (for electrons/positrons) and polarization (for photons). This additional dependence on the discrete quantum numbers prevents the application of the electron/positron spin and photon polarization sum-rules, which significantly simplify the computations in the perturbative regime.Comment: 31 pages, 5 figure

Nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the damping of particle states

In the presence of an electromagnetic background plane-wave field, electron, positron, and photon states are not stable, because electrons and positrons emit photons and photons decay into electron-positron pairs. This decay of the particle states leads to an exponential damping term in the probabilities of single nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. In this paper we investigate analytically and numerically the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the particle states' decay. For this we first compute spin- and polarization-resolved expressions of the probabilities, provide some of their asymptotic behaviors and show that the results of the total probabilities are independent of the spin and polarization bases. Then, we present several plots of the total and differential probabilities for different pulse lengths and for different spin and polarization quantum numbers. We observe that it is crucial to take into account the damping of the states in order for the probabilities to stay always below unity and we show that the damping factors also scale with the intensity and pulse duration of the background field. In the case of nonlinear Compton scattering we show numerically that the total probability behaves like a Poissonian distribution in the regime where the photon recoil is negligible. In all considered cases, the kinematic conditions are such that the final particles momenta transverse to the propagation direction of the plane wave are always much smaller than the particles longitudinal momenta and the main spread of the momentum distribution on the transverse plane is along the direction of the plane-wave electric field.Comment: 44 pages, 12 figure