An operator representation for Matsubara sums

Abstract

In the context of the imaginary-time formalism for a scalar thermal field theory, it is shown that the result of performing the sums 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 the referred operator depends only on the number of internal propagators of the graph. More precisely, it is shown explicitly that this \emph{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.

4 figures; references added, minor changes in notation, final version accepted for publication

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Cited by in corpus (11)

• Isolating vacuum amplitudes in quantum field calculations at finite temperature
• Thermal Operator Representation of Finite Temperature Graphs
• Hard Thermal Loop -- theory and applications
• Thermal Operator Representation of Finite Temperature Graphs II
• The thermal operator representation for Matsubara sums
• Factorization of finite temperature graphs in thermal QED
• Forward scattering amplitudes and the thermal operator representation
• Thermal Operator Representation of Finite-Temperature Amplitudes in the Presence of Chemical Potential
• Thermal Operator and Cutting Rules at Finite Temperature and Chemical Potential
• Nambu-Covariant Many-Body Theory I: Perturbative Approximations
• On the evaluation of Matsubara sums