Hamburg 2001 – scientific programme

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DY: Dynamik und Statistische Physik

DY 43: Kritische Ph
änomene und Phasenumwandlungen

DY 43.1: Talk

Thursday, March 29, 2001, 10:30–10:45, S 7

Recursive Graphical Construction of Tadpole-Free Feynman Diagrams and Their Weights in Φ⁴-Theory — •Axel Pelster, Hagen Kleinert und Konstantin Glaum — Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin

Based on a method developed in the Refs. [1-3], we consider the self-energy and the one-particle irreducible four-point function of the euclidean multicomponent scalar Φ⁴-theory as functionals of the free correlation function. As such they obey a set of functional differential equations which can be turned into graphical recursion relations. They are solved order by order in the number of loops to find all one-particle irreducible Feynman diagrams with their proper weights. A subsequent absorption of the one-loop correction in the lines [4] leads to modified graphical recursion relations for the tadpole-free one-particle irreducible diagrams which are relevant for the renormalization of Φ⁴-theory [5]. Finally, we explain how our procedure is related to a functional Legendre transformation of the free energy with respect to the free correlation function [1].

[1] H. Kleinert, Fortschr. Phys. 30, 187 and 351 (1982).

[2] M. Bachmann, H. Kleinert, A. Pelster, Phys. Rev. D 61, 085017 (2000).

[3] H. Kleinert, A. Pelster, B. Kastening, M. Bachmann, Phys. Rev. E 62, 1537 (2000).

[4] B. Kastening, Phys. Rev. D 54, 3965 (1996).