Operator approach to analytical evaluation of Feynman diagrams

Details Operator approach to analytical evaluation of Feynman diagrams Operator approach to analytical evaluation of Feynman diagrams

2007-09-04

arxiv.org/abs/0709.0419v2

Phys.Atom.Nucl.71:914-924,2008

Physics

High Energy Physics

High Energy Physics - Theory

16 pages. To appear in "Physics of Atomic Nuclei" (Proceedings of SYMPHYS-XII, Yerevan, Armenia, July 03-08, 2006)

Scientific paper

10.1134/S1063778808050219

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.

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