de Mello Koch, R.Ramgoolam, S.2017-04-132017-04-132016-03de Mello Koch, R. and Ramgoolam, S. 2016. Interactions as intertwiners in 4D QFT. Journal of High Energy Physics 2016(3) : Article number 1651126-6708 (Print)1029-8479 (Online)http://hdl.handle.net/10539/22392In a recent paper we showed that the correlators of free scalar field theory in four dimensions can be constructed from a two dimensional topological field theory based on so(4, 2) equivariant maps (intertwiners). The free field result, along with recent results of Frenkel and Libine on equivariance properties of Feynman integrals, are developed further in this paper. We show that the coefficient of the log term in the 1-loop 4-point conformal integral is a projector in the tensor product of so(4, 2) representations. We also show that the 1-loop 4-point integral can be written as a sum of four terms, each associated with the quantum equation of motion for one of the four external legs. The quantum equation of motion is shown to be related to equivariant maps involving indecomposable representations of so(4, 2), a phenomenon which illuminates multiplet recombination. The harmonic expansion method for Feynman integrals is a powerful tool for arriving at these results. The generalization to other interactions and higher loops is discussed.en© 2016 de Mello Koch et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).AdS-CFT CorrespondenceConformal and W SymmetryDuality in Gauge Field TheoriesGauge-gravity correspondenceArticle