#7359. Bold Feynman Diagrams and the Luttinger–Ward Formalism via Gibbs Measures: Perturbative Approach

October 2026publication date
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Journal’s subject area:
Mathematics (miscellaneous);
Analysis;
Mechanical Engineering;
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Abstract:
Many-body perturbation theory is widely used in quantum physics, chemistry, and materials science. At the heart is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the combinatorially growing number of terms of a certain Taylor expansion. In particular, the construction of the ‘bold Feynman diagrammatic expansion’ involves the partial resummation to infinite order of possibly divergent series of diagrams. In this paper, we illustrate how the combinatorial properties of Feynman diagrams in Many-body perturbation theory can be studied in the simplified setting of Gibbs measures and provide a self-contained explanation of Feynman diagrams in this setting.
Keywords:
Feynman diagrams; Luttinger–Ward formalism; perturbative approach

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