Scattering in strong electromagnetic fields: Transverse size effects in time-dependent basis light-front quantization

Abstract

The framework of "time-dependent basis light-front quantization" (tBLFQ) offers a nonperturbative approach to scattering problems in external fields, based on Fock space truncation. Here we extend tBLFQ to include spatio-temporal field inhomogeneities in multiple spacetime directions. This extension is necessary for the proper modeling of e.g. intense laser fields. We focus on the example of nonlinear Compton scattering of an electron on an axicon-type laser, with an emphasis on the transverse structure of the beam. We analyze the impact of field intensity and particle energy, as well as basis truncation effects, on the radiation spectrum of the scattered electron.

Pair production in strong electric fields

“…We define the light-front time and the longitudinal coordinate as x + := x 0 + x 3 and x − := x 0 − x 3 , respectively; the remaining 2 spatial coordinates x ⊥ := x 1 , x 2 are the transverse directions [21,22]. In the light-front formalism of quantum field theory, the time evolution of the system is governed by the light-front Schrödinger equation…”

“…where b is the width of the Gaussian profile in momentum space. This profile corresponds to the lowest state among the 2-dimensional harmonic oscillator (2DHO) eigenstates, which are adopted in our previous tBLFQ studies [21,22]. We plan to expand our transverse basis by including the excited eigenstates of the 2DHO and study the dynamics in the transverse directions in a future study.…”

“…In the numerical implementation of Eq. 7, we adopt the second-order difference scheme MSD2 [21,22,40] rather than the naive "Euler scheme", by relating the state at x + + δx + to those at both x + and x + − δx…”

“…We define the light-front time and the longitudinal coordinate as x + := x 0 + x 3 and x − := x 0 − x 3 , respectively, so dx + dx − = 2dx 0 dx 3 [21,22]. The remaining 2 spatial coordinates x ⊥ := x 1 , x 2 are the transverse directions.…”

“…This approach is thus suitable for studying nonperturbative processes in the presence of strong and possibly time-dependent background fields. The tBLFQ approach has been applied to nonlinear Compton scattering [21,22] in strong electromagnetic fields, to scattering of an electron off a heavy-ion [23] and to scattering of a quark in a color-glass-condensate field modeling a nucleus [24,25]. In this work, we employ tBLFQ to study the pair production process in strong electric fields.…”