Operator approach to analytical evaluation of Feynman diagrams

TL;DR

The paper introduces an operator approach to simplify the analytical evaluation of multi-loop Feynman diagrams, demonstrating its effectiveness on ladder diagrams and potential applications to massive diagrams and integrable models.

Contribution

It presents a novel operator formalism that simplifies existing methods like integration by parts and the star-triangle relation for Feynman diagram evaluation.

Findings

Simplified evaluation of massless Feynman integrals using the operator approach.

Explicit calculation of ladder diagrams in massless $\, ext{phi}^3$ theory.

Potential application to massive diagrams and integrable models.

Abstract

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of "uniqueness" (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless $\phi^3$ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of Lipatov integrable chain model.