Strong-field Breit-Wheeler pair production in ${\mathrm{QED}}_{2+1}$

The Breit-Wheeler pair production process in $2+1$ dimensional spacetime is investigated. In the perturbative regime, nonvanishing rates at the energy threshold are found when odd numbers of photons take part in the reaction. This behavior is understood as a direct consequence of the reduced dimensionality and resembles a corresponding prediction made in gapped graphene monolayers. In the nonperturbative strong field regime, the effect of the dimensionality manifests itself in a different rate dependence on the quantum nonlinearity parameter. The consequence of this deviation is discussed briefly in line with the applicability of perturbation theory. We argue that, in addition to large values of the quantum nonlinearity parameter, the super-renormalizable character of quantum electrodynamics in $2+1$ dimensional spacetime might give rise to a breakdown of perturbation theory within certain energy scales.

Figure 1

Feynman diagram of the Breit-Wheeler pair creation process in a plane-wave background. Here, the wavy line represents a quantized photon, whereas the solid double lines stand for Volkov states of electron and positron.

Figure 2

Feynman diagrams of two (upper panel) and three (lower panel) photons pair creation processes. In both panels, free fermions are represented by external solid lines, and internal lines stand for the free fermion propagators, while wavy lines correspond to photons stemming from quantized and classical sources (the latter are marked by crossed circles).

Figure 3

Dependence of the pair production rate in $2+1$ dimensions on the Mandelstam invariant $s$ for $\eta =0.01$. In the upper panel, the numeric evaluation of the $n=1$ summand of Eq. (18) is depicted in blue, and the corresponding asymptotic expression [see (29)] is colored in red. For comparison, the ${\mathrm{QED}}_{3+1}$ rates for unpolarized, and parallel polarized photons [3] are shown in black solid and black dotted lines, correspondingly. In the lower panel, we compare the outcome of Eq. (31) with the numerically evaluated summand for $n=2$ of Eq. (18), using the same color scheme as in the upper picture.

Figure 4

Dependence of the Breit-Wheeler pair production rate in ${\mathrm{QED}}_{2+1}$ on the quantum nonlinearity parameter $\kappa$ (blue solid line) at asymptotically large value of $\eta$. The corresponding behavior of $R$ for $\kappa \ll 1$ [see Eq. (42)] and $\kappa \gg 1$ [see Eq. (49)] are plotted in purple dotted and red dashed lines, respectively.