▎ 摘　　要

Graphene's low-energy electronic excitations obey a 2+1-dimensional Dirac Hamiltonian. After extending this Hamiltonian to include interactions with a quantized electromagnetic field, we calculate the amplitude associated with the simplest, tree-level Feynman diagram: the vertex connecting a photon with two electrons. This amplitude leads to analytic expressions for the three-dimensional angular dependence of photon emission, the photon-mediated electron-hole recombination rate, and corrections to graphene's opacity pi alpha and dynamic conductivity pi e(2)/2h for situations away from thermal equilibrium, as would occur in a graphene laser. We find that Ohmic dissipation in perfect graphene can be attributed to spontaneous emission.