dorsal/arxiv
View SchemaN-fold Supersymmetry for a Periodic Potential
| Authors | Hideaki Aoyama, Masatoshi Sato, Toshiaki Tanaka, Mariko Yamamoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011009 |
| URL | https://arxiv.org/abs/quant-ph/0011009 |
| DOI | 10.1016/S0370-2693(00)01355-1 |
| Journal | Phys.Lett. B498 (2001) 117-122 |
Abstract
We report a new type of supersymmetry, "N-fold supersymmetry", in one-dimensional quantum mechanics. Its supercharges are N-th order polynomials of momentum: It reduces to ordinary supersymmetry for N=1, but for other values of N the anticommutator of the supercharges is not the ordinary Hamiltonian, but is a polynomial of the Hamiltonian. (For this reason, the original Hamiltonian is referred to as the "Mother Hamiltonian".) This supersymmetry shares some features with the ordinary variety, the most notable of which is the non-renormalization theorem. An N-fold supersymmetry was earlier found for a quartic potential whose supersymmetry is spontaneously broken. Here we report that it also holds for a periodic potential, albeit with somewhat different supercharges, whose supersymmetry is not broken.
{
"annotation_id": "2e5529ea-fcad-4e2a-983c-dfd57edccd94",
"date_created": "2026-03-02T18:01:41.783000Z",
"date_modified": "2026-03-02T18:01:41.783000Z",
"file_hash": "d7a29e45d245598619431cae896a3f32ac0f548e72a552adb69b39674f10f1b8",
"private": false,
"record": {
"abstract": "We report a new type of supersymmetry, \"N-fold supersymmetry\", in\none-dimensional quantum mechanics. Its supercharges are N-th order polynomials\nof momentum: It reduces to ordinary supersymmetry for N=1, but for other values\nof N the anticommutator of the supercharges is not the ordinary Hamiltonian,\nbut is a polynomial of the Hamiltonian. (For this reason, the original\nHamiltonian is referred to as the \"Mother Hamiltonian\".) This supersymmetry\nshares some features with the ordinary variety, the most notable of which is\nthe non-renormalization theorem. An N-fold supersymmetry was earlier found for\na quartic potential whose supersymmetry is spontaneously broken. Here we report\nthat it also holds for a periodic potential, albeit with somewhat different\nsupercharges, whose supersymmetry is not broken.",
"arxiv_id": "quant-ph/0011009",
"authors": [
"Hideaki Aoyama",
"Masatoshi Sato",
"Toshiaki Tanaka",
"Mariko Yamamoto"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1016/S0370-2693(00)01355-1",
"journal_ref": "Phys.Lett. B498 (2001) 117-122",
"title": "N-fold Supersymmetry for a Periodic Potential",
"url": "https://arxiv.org/abs/quant-ph/0011009"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c4a6b575-40f0-4179-abba-e89dba80f41c",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}