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| Format: | Recurso digital |
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Zenodo
2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.20241558 |
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Inhaltsangabe:
- <p>This article introduces a <strong>gauge-covariant wavelet transform for plaquette curvatures on lattices</strong>. The construction is designed for lattice gauge fields with values in a compact matrix Lie group and addresses a basic difficulty: ordinary wavelet decompositions applied directly to link variables are not compatible with gauge transformations.</p> <p>Instead of decomposing link variables, the paper works with plaquette holonomies and their local logarithmic curvatures in a small-field regime. These curvatures are interpreted as elements of a discrete adjoint bundle, transported to a common base point inside each local cell, and then decomposed using a real orthonormal wavelet basis on the plaquette index set.</p> <p>The resulting wavelet coefficients are Lie-algebra-valued and transform covariantly under gauge transformations. The article proves gauge covariance, local reconstruction of plaquette holonomies, a Parseval identity, gauge-invariant scale-wise energies for fixed trivializations, and independence of the total Parseval energy under changes of trivialization.</p> <p>The work also discusses intercell comparison by parallel transport, changes of local trivialization, compatibility with the discrete Bianchi identity, an abelian cohomological characterization on contractible regions, and elementary examples for abelian and non-abelian gauge groups.</p> <p>The article is intended as a mathematical framework for multiscale analysis of lattice gauge curvature, providing a bridge between wavelet methods, discrete geometry, and gauge-covariant field analysis.</p>