Perturbative Results Without Diagrams

Abstract

Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature from the cumulant expansion of the corresponding observable followed by an extrapolation to zero temperature. This method (originally proposed by Bogolyubov and Plechko) is applied to the calculation of higher-order terms for the ground-state energy of the polaron. Using state-of-the-art multidimensional integration routines 2 new coefficients are obtained corresponding to a 4- and 5-loop calculation.Comment: 6 pages, 2 figures, WS style (included), to be published in Proceedings of "Path Integrals - New Trends and Perspectives", Dresden (Germany), Sept. 23 - 28, 200