{"paper":{"title":"On the Fast Fourier Transform on SU(2)","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP","math.NA","quant-ph"],"primary_cat":"physics.comp-ph","authors_text":"Alejandro Uma\\~na, Julio Delgado","submitted_at":"2026-04-19T17:38:38Z","abstract_excerpt":"The special unitary group SU(2) plays a fundamental role in the description of symmetries in quantum mechanics, theoretical physics, and spherical signal processing. In this paper, we address the computational challenges of performing spectral analysis on this non-abelian compact Lie group. We present the Fourier Transform (FT) on SU(2) and develop a Fast Fourier Transform (FFT) algorithm inspired by the classical Cooley-Tukey divide-and-conquer scheme. Our approach efficiently discretizes the group using Euler angles, applying a two-dimensional FFT on the angular variables and exploiting the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23923","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23923/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}