{"paper":{"title":"Polynomial solution of quantum Grassmann matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Miguel Tierz","submitted_at":"2017-03-07T16:21:08Z","abstract_excerpt":"We study a model of quantum mechanical fermions with matrix-like index structure (with indices $N$ and $L$) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with $q$-deformed orthogonal polynomials (Stieltjes-Wigert polynomials), for different values of $L$ and arbitrary $N$. From the explicit evaluation of the thermal partition function, the energy levels and degeneracies are determined. For a given $L$, the number of states of different energy is quadratic in $N$, which implies an exponential degeneracy of the energy levels. We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02454","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"}