The free energy of the Coulomb gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds to a renormalization of the two-point vertex function. By collecting together the leading-order logarithmic corrections we have derived the standard result for the density of states for the critical dimension, . This method, which is shown to be identical to the approach of Thouless, Anderson and Palmer to spin glasses, allows us to derive the strong-disorder behaviour of the density of states. The use of the renormalization group allows this derivation to be extended to all disorders, and the use of an -expansion allows the method to be extended to and . We speculate that the renormalization group equations can also be derived diagrammatically, allowing a simple derivation of the crossover behaviour observed in the case of weak disorder.