2003/05/31 by Olivier Espinosa, Edgardo Stockmeyer · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Computer science #Correctness #Cosmology and Gravitation Theories #Diagrammatic reasoning #Discrete mathematics #Feynman diagram #Graph #Mathematical physics #Mathematics #Operator (biology) #Propagator #Pure mathematics #Quantum, superfluid, helium dynamics #Vertex (graph theory) #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.69.065004
published as Phys.Rev. D69 (2004) 065004 · 4 figures; references added, minor changes in notation, final version accepted for publication
arxiv created 2003/12/11 · openalex publication_date 2004/03/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the context of the imaginary-time formalism for scalar thermal field theory, it is shown that the result of performing the summations over Matsubara frequencies associated with loop Feynman diagrams can be written, for some classes of diagrams, in terms of the action of a simple linear operator on the corresponding energy integrals of the Euclidean theory at T=0. In its simplest form this operator depends only on the number of internal propagators of the graph. More precisely, it is shown explicitly that this ``thermal operator representation'' holds for two generic classes of diagrams: namely, the two-vertex diagram with an arbitrary number of internal propagators and the one-loop diagram with an arbitrary number of vertices. The validity of the thermal operator representation for diagrams of more complicated topologies remains an open problem. Its correctness is shown to be equivalent to the correctness of some diagrammatic rules proposed a few years ago.