Abstract
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.
Highlights
There is a growing interest in testing QED under the extreme conditions provided by intense laser fields [1,2,3,4,5,6,7]
The effects of the decay of the states, are cumulative effects scaling with the laser pulse duration and amount to exponential damping factors, which take into account the fact that Volkov electron/ positron states and free photon states are not stable states in a plane wave, once the interaction between the electron/ positron Dirac field and the electromagnetic field is taken into account
After solving the Schwinger-Dyson equations for electron, positron, and photon in- and out-states, we have inserted them into the leading order in α amplitudes of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production to determine the effects of the states decay into the corresponding probabilities
Summary
There is a growing interest in testing QED under the extreme conditions provided by intense laser fields [1,2,3,4,5,6,7]. The conclusion of the above discussion is that, if one would like to take into account accumulation effects depending on the laser pulse duration in nonlinear Compton scattering and in nonlinear Breit-Wheeler pair production but still neglect corrections scaling only with α, one could solve the Schwinger-Dyson equations with the one-loop mass operator and polarization operator, find the corresponding electron/positron and photon states including the decaying effects, and use these states to compute the probabilities as the modulus square of the single-vertex. We derive the Schwinger-Dyson equations for the electron and photon out-states as well as for the positron in- and out-states, and we provide the corresponding solutions under the mentioned conditions We use these in- and out-states to derive analytical expressions of the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production, which feature exponential damping terms describing the decay of the particles in the plane wave
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