dorsal/arxiv
View SchemaStatistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404025 |
| URL | https://arxiv.org/abs/quant-ph/0404025 |
| DOI | 10.1088/0305-4470/37/43/012 |
| Journal | J.Phys.A37:10193-10208,2004 |
Abstract
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N=2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (non-equivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie algebras, and study multi-particle systems of abnormal phermions. The latter provides a certain bosonization of multi-fermion systems.
{
"annotation_id": "675ef4ee-cb37-4d4f-aaa2-d4fb34ef21ec",
"date_created": "2026-03-02T18:02:06.346000Z",
"date_modified": "2026-03-02T18:02:06.346000Z",
"file_hash": "48b9489bb5805982b7702d58022dd6c558980cfcc9d8db967de65bd8d1c19249",
"private": false,
"record": {
"abstract": "We show that the metric operator for a pseudo-supersymmetric Hamiltonian that\nhas at least one negative real eigenvalue is necessarily indefinite. We\nintroduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras\nand provide a pair of basic realizations of the algebra of N=2\npseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is\nidentified with either a boson-phermion or a boson-abnormal-phermion exchange\nsymmetry. We further establish the physical equivalence (non-equivalence) of\nphermions (abnormal phermions) with ordinary fermions, describe the underlying\nLie algebras, and study multi-particle systems of abnormal phermions. The\nlatter provides a certain bosonization of multi-fermion systems.",
"arxiv_id": "quant-ph/0404025",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/37/43/012",
"journal_ref": "J.Phys.A37:10193-10208,2004",
"title": "Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions",
"url": "https://arxiv.org/abs/quant-ph/0404025"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ee103939-895b-41c9-b987-548687a13fe5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}