{"paper":{"title":"Nonuniform symmetry breaking in noncommutative $\\lambda \\Phi^4$ theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"D. Zappala', P. Castorina","submitted_at":"2003-03-04T17:42:39Z","abstract_excerpt":"The spontaneous symmetry breaking in noncommutative $\\lambda\\Phi^4$ theory has been analyzed by using the formalism of the effective action for composite operators in the Hartree-Fock approximation. It turns out that there is no phase transition to a constant vacuum expectation of the field and the broken phase corresponds to a nonuniform background. By considering $<\\phi(x)>=A \\cos(\\vec Q \\cdot \\vec x)$ the generated mass gap depends on the angles among the momenta $\\vec k$ and $\\vec Q$ and the noncommutativity parameter $\\vec\\theta$. The order of the transition is not easily determinable in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0303030","kind":"arxiv","version":2},"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"}