Parts | Days | Selection | Search | Updates | Downloads | Help
Q: Fachverband Quantenoptik und Photonik
Q 24: Poster II
Q 24.10: Poster
Tuesday, March 12, 2024, 17:00–19:00, KG I Foyer
Resummations of the two-particle irreducible quantum effective action — •Hannes Köper1 and Thomas Gasenzer1,2 — 1Kirchhoff-Institut für Physik, Im Neuenheimer Feld 227, 69120 Heidelberg — 2Institut für Theoretische Physik, Philosophenweg 16, 69120 Heidelberg
The two-particle irreducible quantum effective action can be formulated in terms of the Luttinger-Ward functional, which is diagrammatically given by the series of all two-particle irreducible vacuum Feynman diagrams. In this work, we reformulate infinite series of vacuum Feynman diagrams for scalar quantum field theories, whose potentials admit discrete frequency spectra such as the sine-Gordon model, in terms of spin systems on graphs. While the frequencies of the potential directly correspond to the possible spin values, the graph’s topology is tightly connected to the class of vacuum diagrams that is being summed over. Different graph topologies thus correspond to different selective resummations of diagrams. In particular, cycle graphs correspond to "ring"-type resummations often encountered in next-to-leading order in 1/N expansions. This allows us to compute a closed form expression for the Luttinger-Ward functional within "ring-approximation" in terms of the eigenvalues of an associated transfer operator. We also present how the formalism may be applied to polynomial and O(N)-symmetric potentials.
Keywords: Resummation; Feynman diagrams; Sine-Gordon-type models; Two-particle irreducible; Self-energy