S. H. Djah | Searcharxiv

arXiv2006

Feynman graphs for non-Gaussian measures

Partition- and moment functions for a general (not necessarily Gaussian) functional measure that is perturbed by a Gibbs factor are calculated using generalized Feynman graphs. From the graphical calculus, a new notion of Wick ordering arises, that coincides with orthogonal decompositions of Wiener-Itô type only if the measure is Gaussian. Proving a generalized linked cluster theorem, we show that the logarithm of the partition function can be expanded in terms of connected Feynman graphs ("linked cluster theorem").

math-ph↗

arXiv2004

Feynman graph representation of the perturbation series for general functional measures

A representation of the perturbation series of a general functional measure is given in terms of generalized Feynman graphs and -rules. The graphical calculus is applied to certain functional measures of Lévy type. A graphical notion of Wick ordering is introduced and is compared with orthogonal decompositions of the Wiener-Itô-Segal type. It is also shown that the linked cluster theorem for Feynman graphs extends to generalized Feynman graphs. We perturbatively prove existence of the thermodynamic limit for the free energy density and the moment functions. The results are applied to the gas of charged microscopic or mesoscopic particles -- neutral in average -- in $d=2$ dimensions generating a static field $ϕ$ with quadratic energy density giving rise to a pair interaction. The pressure function for this system is calculated up to fourth order. We also discuss the subtraction of logarithmically divergent self-energy terms for a gas of only one particle type by a local counterterm of first order.

math-ph↗