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arXiv:2605.28528

Electron-photon interaction: Feynman diagrams and contact points

Lev Sakhnovich

math-phquant-phSubmitted May 27, 2026• Announced May 28, 2026
arXivHTMLPDF

Abstract

In this note, we formulate the notions of the direct and inverse problems and contact points for the Feynman diagrams. For the electron-photon interaction case, the solutions of these direct and inverse problems are presented. The interrelations between Feynman diagrams and the classical colored graphs are discussed.
Comments
This note is a prolongation of our works arXiv:2511.02847 and arXiv:2604.11612 on Feynman's theory although in a somewhat different context

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The Sachdev-Ye-Kitaev (SYK) model is a model of qqq interacting fermions whose large N limit is dominated by melonic graphs. In this review we first present a diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs. Gross and Rosenhaus have then proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, these flavors can be seen as reminiscent of the colors used in random tensor theory. Applying modern tools from random tensors to such a colored SYK model, all leading and next-to-leading orders diagrams of the 2-point and 4-point functions in the large NNN expansion can be identified. We then study the effect of non-Gaussian average over the random couplings in a complex, colored version of the SYK model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in NNN. We then derive the form of the effective action to all orders.