Fundamental theory is developed for three-body resonance energy transfer in the condensed phase, involving two donors and a single acceptor. This energy pooling mechanism is responsible for recent experimental observations on trichromophore molecules and other moieties, manifest for example in the photochemistry of organo dyes and rare-earth ion doped crystals. A full quantum electrodynamical (QED) treatment of this pooling is developed and formulated with the aid of a novel diagrammatic method, which proves to have several advantages over Feynman diagram methods. Following derivation of the rate of energy pooling for an isolated group of chromophores, the electronic influences of the medium across which the energy migrates are embedded in the theory and duly discussed. Energetic constraints on the acceptor molecule are elucidated and shown to account for a variety of postulated mechanisms: the geometry of the three-center system is itself shown to exercise considerable control over the dominant mechanism. By extension, the theory is amenable to the study of more complex energy transfer arrangements, such as those observed in dendrimer chemistry and the light-harvesting photochemistry of the photosynthetic unit.