Recursive graphical construction of Feynman diagrams and their multiplicities in φ4 and φ2A theory

Hagen Kleinert, Axel Pelster, Boris Kastening, and Michael Bachmann
Phys. Rev. E 62, 1537 – Published 1 August 2000
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Abstract

The free energy of a field theory can be considered as a functional of the free correlation function. As such it obeys a nonlinear functional differential equation that can be turned into a recursion relation. This is solved order by order in the coupling constant to find all connected vacuum diagrams with their proper multiplicities. The procedure is applied to a multicomponent scalar field theory with a φ4 self-interaction and then to a theory of two scalar fields φ and A with an interaction φ2A. All Feynman diagrams with external lines are obtained from functional derivatives of the connected vacuum diagrams with respect to the free correlation function. Finally, the recursive graphical construction is automatized by computer algebra with the help of a unique matrix notation for the Feynman diagrams.

  • Received 21 July 1999

DOI:https://doi.org/10.1103/PhysRevE.62.1537

©2000 American Physical Society

Authors & Affiliations

Hagen Kleinert1, Axel Pelster1, Boris Kastening2, and Michael Bachmann1

  • 1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
  • 2Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

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Vol. 62, Iss. 2 — August 2000

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