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h4lat computes the Clebsch-Gordan coefficients of the hypercubic group ${H(4)}$ and builds ${H(4)}$-irreducible lattice operators ${\bar\psi \, \Gamma \, D \cdots D \, \psi}$, with ${\Gamma = \mathbf{1}, \gamma_5, \gamma_\mu, \gamma_\mu\gamma_5, \sigma_{\mu\nu}}$, for lattice QCD calculations of the moments of parton distribution functions. For every operator it gives the kinematic factor, the C-parity, the trace condition and the index symmetry.

This wiki is the documentation of h4lat: a user guide, the group theory behind the library, and the references.

Where to start

If you want to…	Read
install h4lat	Installation
understand the group theory and the method	The hypercubic group → Clebsch-Gordan coefficients → Lattice operators
decompose tensor products and get Clebsch-Gordan coefficients	Computing Clebsch-Gordan coefficients
use the 1360 bundled operators	Operator database and Building operators
browse the operators in a PDF	Operator catalogue
reproduce the operators of a published paper	Operators from the literature
save a selection of operators	Saving and loading operators
find a function	API overview

The Jupyter notebooks in the examples/ folder show the library at work.

A first example

from h4lat import get_OperatorList, latex_print_multiplicities

# (4,1) ⊗ (4,1): the vector operators with one derivative, ψ̄ γ_μ D_ν ψ
print(latex_print_multiplicities((4, 1), (4, 1)))

# the same operators from the bundled database, with their irrep, C-parity and kinematic factor
for op in get_OperatorList(keys="V1"):
    print(op.id, op.irrep, op.C, op.K)

Versions

The wiki describes the code on the main branch. Features listed under "Unreleased" in the changelog are not yet in the release on PyPI. Operator IDs and conventions can change between versions: the changelog lists every change, and the wiki notes the ones that affect results ("Until October 2026 …").

Citing, questions and contributions

If you use h4lat in your research, please cite it as explained in the README, giving the version you used. Questions, bug reports and suggestions are welcome as GitHub issues, and CONTRIBUTING.md explains how to contribute, also to this wiki.