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Description
In certain cases, the problem of evaluating a Feynman diagram can be reduced to the study of a specific (graph-building) operator. This approach is particularly effective for diagrams with a recursive structure. For example, the proof of the remarkable Basso–Dixon determinant formula for fishnet correlators was obtained by exploiting the underlying integrable structure of a system of such operators. Apparently, there is another operator-based technique for evaluating Feynman diagrams which relies on their connection with Green’s functions of specific quantum-mechanical systems. In the talk, I will give an overview of how these two operator-based methods can be combined. After introducing the key ideas, I will briefly comment on applications to the two-loop master diagram and the zig-zag series in \varphi^4 theory, and then focus on conformal four-point ladder diagrams. In the latter case, I will discuss how the obtained representation can be used to derive dimensional and loop-shift identities, express the results in terms of classical polylogarithms, and regularize divergences arising for specific propagator powers.
