Kleinert, Hagen ; Pelster, Axel ; Kastening, Boris ; Bachmann, Michael (2000)
Recursive graphical construction of Feynman diagrams and their multiplicities in φ^{4} and φ^{2}A theory.
In: Physical Review E, 62 (2)
doi: 10.1103/PhysRevE.62.1537
Artikel, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2000 |
| Autor(en): | Kleinert, Hagen ; Pelster, Axel ; Kastening, Boris ; Bachmann, Michael |
| Art des Eintrags: | Bibliographie |
| Titel: | Recursive graphical construction of Feynman diagrams and their multiplicities in φ^{4} and φ^{2}A theory |
| Sprache: | Englisch |
| Publikationsjahr: | August 2000 |
| Verlag: | American Physical Society |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Physical Review E |
| Jahrgang/Volume einer Zeitschrift: | 62 |
| (Heft-)Nummer: | 2 |
| DOI: | 10.1103/PhysRevE.62.1537 |
| Kurzbeschreibung (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. |
| Fachbereich(e)/-gebiet(e): | 11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft > Fachgebiet Dünne Schichten 11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft 11 Fachbereich Material- und Geowissenschaften |
| Hinterlegungsdatum: | 04 Jan 2013 11:34 |
| Letzte Änderung: | 05 Mär 2013 10:04 |
| PPN: | |
| Sponsoren: | M.B. and B.K. acknowledge support by the Studienstiftung des deutschen Volkes and the Deutsche Forschungsgemeinschaft (DFG), respectively. |
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