Perturbation Theory Without Diagrams: The Polaron Case

Details Perturbation Theory Without Diagrams: The Polaron Case Perturbation Theory Without Diagrams: The Polaron Case

2008-05-29

arxiv.org/abs/0805.4525v2

Phys.Rev.E79:016705,2009

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, 7 figures, 4 tables, Latex, v2: misprints corrected, small changes in text following referee comments and PR style c

Scientific paper

10.1103/PhysRevE.79.016705

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 two new coefficients are obtained corresponding to a four- and five-loop calculation. Several analytical and numerical procedures have been implemented which were crucial for obtaining reliable results.

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