#7360. Bold Feynman Diagrams and the Luttinger–Ward Formalism Via Gibbs Measures: Non-perturbative Analysis

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. This procedure demands investigation from both the combinatorial (perturbative) and the analytical (non-perturbative) viewpoints. In this paper, we approach the analytical investigation of the bold diagrammatic expansion in the simplified setting of Gibbs measures.
Keywords:
Feynman Diagrams; Luttinger–Ward Formalism; non-perturbative analysis

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