QFT applications of (multi-dimensional) Mellin-Barnes representation: asymptotic expansions, analytic continuation and more

par David Greynat (Universidad de Zaragoza)

jeudi 24 nov. 2011, 11:00 → 12:00 Europe/Paris

Auditorium M. Vivargent (LAPTH)

The Mellin-Barnes (MB) integral representation is a very powerful tool of asymptotic analysis. In the one-dimensional case (where one deals with a single MB integral depending on one parameter), it allows for an easy analytic evaluation, to an arbitrary order, of the asymptotic expansions in powers and logs of the parameter of the quantity expressed initially as a MB integral. Applications of this formalism in QFT are varied: evaluation of Feynman diagrams and related quantities, calculations of non-perturbative contributions, reconstructions of non-analytic functions, etc. After a short panorama of the possibilities offered by the MB representation, illustrated with some examples taken in perturbative QFT, heavy quark physics and simple models, we will concentrate on the presentation of some recent results obtained in the case of multi-dimensional MB integrals depending on several parameters. In this interesting generalization, one may usually obtain several multiple series representations of a given multiple MB integral. Basing our presentation on simple QFT integrals we will address the question concerning the convergence of such series as well as their analytic continuation.

Slides Greynat