Operators from the literature

get_paper_operators returns the ${H(4)}$-irreducible operators used in published works. Select the paper by its INSPIRE texkey or by its DOI. Each operator's id is its label in the paper:

from h4lat import AVAILABLE_PAPERS, get_paper_operators

print(AVAILABLE_PAPERS)                                       # INSPIRE texkey -> DOI

ops = get_paper_operators("Rodekamp:2023wpe")                 # by INSPIRE texkey
ops = get_paper_operators(doi="10.1103/PhysRevD.109.074508")  # by DOI: the same operators

for op in ops:
    print(f"id={op.id}  X={op.X}  irrep={op.irrep}  C={op.C}")
    op.display()   # renders LaTeX in a Jupyter notebook

Available papers

INSPIRE texkey	Reference	Operators
Burger:2021knd	S. Bürger et al., Phys. Rev. D 105, 054504 (2022), arXiv:2111.08306	a₂: axial, irrep (4,3), 2 derivatives; d₂: axial, irrep (8,1), 2 derivatives, and tensor, irrep (8,1), 1 derivative
Rodekamp:2023wpe	M. Rodekamp et al., Phys. Rev. D 109, 074508 (2024), arXiv:2401.05360	1 derivative: vector, irreps (3,1) and (6,3); axial, irrep (6,4); tensor, irreps (8,1) and (8,2)
Taggi:2026skn	E. Taggi et al., Phys. Rev. D 114, 074507 (2026), arXiv:2605.02808	2 derivatives: vector, irrep (4,2); axial, irrep (4,3); tensor, irreps (3,2), (3,3) and (6,2)
Alexandrou:2026tjs	C. Alexandrou et al., arXiv:2607.03458 (2026)	vector: 2 derivatives, irrep (4,2); 3 derivatives, irreps (1,2) and (6,2)
Gockeler:2004wp	M. Göckeler et al., Phys. Rev. D 71, 114511 (2005), arXiv:hep-ph/0410187	vector: 1 derivative, irreps (6,3) and (3,1); 2 derivatives, irrep (8,1); 3 derivatives, irrep (2,1)
LHPC:2002xzk	D. Dolgov et al. (LHPC and SESAM), Phys. Rev. D 66, 034506 (2002), arXiv:hep-lat/0201021	vector: 1 derivative, irreps (6,3) and (3,1); 2 derivatives, irrep (8,1); 3 derivatives, irrep (2,1); axial: no derivative, irrep (4,4); 1 derivative, irreps (6,4) and (6,1); 2 derivatives, irreps (4,3) and (8,1); tensor: no derivative, irrep (6,1); 1 derivative, irrep (8,1)
Gockeler:1995wg	M. Göckeler et al., Phys. Rev. D 53, 2317 (1996), arXiv:hep-lat/9508004	vector: 1 derivative, irreps (6,3) and (3,1); 2 derivatives, irrep (8,1); 3 derivatives, irrep (2,1); axial: no derivative, irrep (4,4); 2 derivatives, irreps (4,3) and (8,1)

The test suite checks the labels, Dirac structures, irreps and C-parities of the operators of every paper. For the papers of Göckeler et al. and Dolgov et al., it also compares the operators with the expressions given in the papers, and their kinematic factors with the papers' kinematics.

How the operators are built

Each operator is a linear combination of operators of the bundled database (Operator_from_database(id)), built with the operator arithmetic. The notebook paper_operators.ipynb shows the code that builds the operators of each paper. Combining the catalogue operators differently gives the operator basis of other works: contributions of new papers are welcome (see CONTRIBUTING.md).

For operators free of mixing under renormalisation, see also get_op_selection and the theory page Lattice operators.