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Many-loop calculations: The uniqueness method and functional equations

D. I. Kazakov


Abstract: In the framework of the calculation of many-loop Feynman integrals – the uniqueness method – functional equations are obtained for the coefficient functions of the diagrams. Solution of a functional equation leads to calculation of an $N$-shaped diagram, the last of the 5-loop diagrams of the $\varphi^4$ theory. The obtained result makes it possible to extend by an order the tables constructed previously for the calculation of many-loop integrals.

Received: 16.01.1984

 English version: Theoretical and Mathematical Physics, 1985, 62:1, 84–89

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