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arXiv · 2401.01682

Conservation, crossing symmetry, and completeness in diagrammatic theories

Frederick Green
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Abstract

The diagrammatic analysis of interacting particle assemblies harbors a fundamental mismatch between two of its main implementations: Phi-derivable (conserving) approximations and parquet (crossing symmetric) models. No termwise expansion, short of the exact theory itself, can be both conserving and crossing symmetric. This work applies the Kraichnan embedded-Hamiltonian formalism for strongly coupled systems to investigate consistency of the interplay between purely pair-mediated correlations and pair-irreducible ones. The approach sheds a different light on the issue of crossing symmetry versus conservation. In the process, the parquet equations acquire a different formulation.

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Frederick Green. 2024-01-03. Conservation, crossing symmetry, and completeness in diagrammatic theories. https://doi.org/10.1103/physreva.110.052222

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