Perturbation Theory Without Diagrams: The Polaron Case

Understand

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.