  Low-energy single-electron dynamics in graphene monolayers and similar
nanostructures is described by the Dirac model, being a 2+1 dimensional version
of massless QED with the speed of light replaced by the Fermi velocity
v_{F}=c/300. Methods of strong-field QFT are relevant for the Dirac model,
since any low-frequency electric field requires a nonperturbative treatment of
massless carriers in case it remains unchanged for a sufficiently long time
interval. In this case, the effects of creation and annihilation of
electron-hole pairs produced from vacuum by a slowly varying and small-gradient
electric field are relevant, thereby substantially affecting the radiation
pattern. For this reason, the standard QED text-book theory of photon emission
cannot be of help. We construct the Fock-space representation of the Dirac
model, which takes exact accounts of the effects of vacuum instability caused
by external electric fields, and in which the interaction between electrons and
photons is taken into account perturbatively, following the general theory (the
generalized Furry representation). We consider the effective theory of photon
emission in the first-order approximation and construct the corresponding total
probabilities, taking into account the unitarity relation.
