{"paper":{"title":"Contraction of broken symmetries via Kac-Moody formalism","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jamil Daboul","submitted_at":"2006-08-02T15:20:26Z","abstract_excerpt":"I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard 2-D Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was denoted by ${\\mathbb H}_2 $, gets reduced by the symmetry breaking term, defined by the Hamiltonian \\[ H(\\beta)= \\frac 1 {2m} (p_1^2+p_2^2)- \\frac \\alpha r - \\beta r^{-1/2} \\cos ((\\phi-\\gamma)/2). \\] For this $H (\\beta)$ I define two symmetry loop algebras ${\\mathfrak L}_{i}(\\beta), i=1,2$, by choosing the `basic generators' differently. These ${\\mathfrak L}_{i}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0608008","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":""},"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"}