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, non-vanishing rates at the energy threshold are found when odd numbers of photons take part on the reaction. This behaviour is understood as a direct consequence of the reduced dimensionality and resembles a corresponding prediction made in gapped graphene monolayers. In the non-perturbative strong field regime the effect of the dimensionality manifests itself in a different rate dependence on the quantum non-linearity 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 non-linearity parameter, the superrenormalisable character of quantum electrodynamics in $2+1$ dimensional spacetime might give rise to a breakdown of perturbation theory within certain energy scales.
Comment: 12 pages, 4 figures