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Recursive graphical construction of Feynman diagrams and their multiplicities in φ^{4} and φ^{2}A theory

Kleinert, Hagen and Pelster, Axel and Kastening, Boris and Bachmann, Michael (2000):
Recursive graphical construction of Feynman diagrams and their multiplicities in φ^{4} and φ^{2}A theory.
In: Physical Review E, American Physical Society, pp. 1537-1559, 62, (2), ISSN 1063-651X, [Online-Edition: http://dx.doi.org/10.1103/PhysRevE.62.1537],
[Article]

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.

Item Type: Article
Erschienen: 2000
Creators: Kleinert, Hagen and Pelster, Axel and Kastening, Boris and Bachmann, Michael
Title: Recursive graphical construction of Feynman diagrams and their multiplicities in φ^{4} and φ^{2}A theory
Language: English
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.

Journal or Publication Title: Physical Review E
Volume: 62
Number: 2
Publisher: American Physical Society
Divisions: 11 Department of Materials and Earth Sciences > Material Science > Advanced Thin Film Technology
11 Department of Materials and Earth Sciences > Material Science
11 Department of Materials and Earth Sciences
Date Deposited: 04 Jan 2013 11:34
Official URL: http://dx.doi.org/10.1103/PhysRevE.62.1537
Identification Number: doi:10.1103/PhysRevE.62.1537
Funders: M.B. and B.K. acknowledge support by the Studienstiftung des deutschen Volkes and the Deutsche Forschungsgemeinschaft (DFG), respectively.
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