Discrete worldline instantons

Abstract

The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion, i.e. worldline instantons, is possible analytically only in special cases, and a numerical treatment is nontrivial as well. We introduce a completely general numerical approach based on an approximate evaluation of the discretized path integral that easily and robustly gives the full semiclassical pair production rate in nontrivial multi-dimensional fields, and apply it to some example cases.

Perturbative methods for assisted nonperturbative pair production

“…This allows us to find simple, explicit analytical approximations. As shown in [7,45], purely time-dependent fields can, at least in some regimes, be used to give good quantitative approximations. It is also useful to start with such fields because it allows us to compare with the exact result obtained with well-developed numerical methods like solving the Riccati equation, which can be done to high precision [36], or the Wigner/quantum kinetic theory, which could be used for e.g.…”

“…This could be useful for searching for promising parameter values for maximizing the enhancement of the probability for future experiments, before turning to a fully numerical treatment [10,[48][49][50][51]. Moreover, as demonstrated in [45] and [52], knowing the saddle points for some simpler fields can be very useful for finding the corresponding ones for complex fields that can be reached via a continuous deformation, which gives further motivation for working out all the details for simple fields as a start.…”

Small-scale structure of fuzzy and axion-like dark matter

“…The 21 cm HI absorption signal reported by the EDGES experiment was used to constrain the FDM mass to m ≥ 5 × 10 −21 eV [120] and m ≥ 8 × 10 −21 eV [121] (see also [122] for a recent analysis). These are the strongest bounds to date that follow from the low-mass cutoff of the halo mass function.…”

Single and double nonlinear Compton scattering

“…The gluing approach works if (42) gives (41) after summing over n 1 . In (40) we have only used 1 = 1 and n = 0. For linear polarization with a ∝ e 1 we have X·V = 0, and then we can simply sum over n 1 = ±e 2 .…”