We present a general representation for solving problems in many-body perturbation theory. By projecting the single-particle Green's function to an auxiliary space, we show how one can convert an arbitrary Feynman graph to a universal kernel representation. Once constructed, the computation kernel contains no problem-specific information yet contains all explicit temperature and frequency dependence of the diagram. This computation kernel is problem agnostic, and valid for any physical problem that would normally leverage the Matsubara formalism of many-body perturbation theory. The result of any diagram can be written as a linear combination of these computation kernel elements with coefficients given by a sum over products of known tensor elements that are themselves problem-specific and represent spatial degrees of freedom. We probe the efficacy of this approach by generating the computation kernel for a low-order self-energy diagram, which we then use to construct solutions to distinct problems.

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• Feynman diagrams
• Quantum many-body systems
• Approximation methods for many-body systems
• Diagrammatic methods
• Hubbard model