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Juggling with Tensor Bases in Functional Approaches

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arxiv 2503.05580 v1 pith:HGZVC4QE submitted 2025-03-07 hep-th cond-mat.str-elhep-ph

classification hep-thcond-mat.str-elhep-ph
keywords basestensorapproacheselementsfunctionaltasksverticesaforementioned
verification ladder T0 review T1 audit T2 compute T3 formal

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Systematic expansion schemes in functional approaches require the inclusion of higher order vertices. These vertices are expanded in independent tensor bases with a rapidly increasing number of basis elements. Amongst the related tasks are the construction of bases and projection operators, the importance ordering of their elements, and the optimisation of such tensor bases, as well as an analysis of their regularity in momentum space. We present progress in all these directions and introduce the Mathematica package TensorBases designed for the aforementioned tasks.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Pion Distribution Amplitudes from Functional QCD

    hep-ph 2026-07 conditional novelty 7.0 of 10

    The pion DA computed from functional QCD via LaMET has ⟨ξ²⟩_π = 0.267 (no quoted error), consistent with sum rules and DSE/BSE and 0.8σ below the lattice-LaMET value 0.300(41).

  2. Getting a handle on correlation functions

    hep-ph 2026-02 accept novelty 3.0 of 10

    A pedagogical guide to constructing symmetry-adapted tensor bases and momentum variables for n-point correlation functions in Euclidean quantum field theory.

  3. A beginner's guide to functional methods in particle physics

    hep-ph 2025-10 accept novelty 1.0 of 10

    A pedagogical review showing how Dyson-Schwinger, 3PI, and Bethe-Salpeter equations can be chained together to compute glueball masses in pure Yang-Mills theory, matching lattice QCD.

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