dorsal/arxiv
View SchemaSupersymmetric Quantum Mechanics with a Point Singularity
| Authors | Takashi Uchino, Izumi Tsutsui |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210084 |
| URL | https://arxiv.org/abs/quant-ph/0210084 |
| DOI | 10.1016/S0550-3213(03)00352-3 |
| Journal | Nucl.Phys.B662:447-460,2003 |
Abstract
We study the possibility of supersymmetry (SUSY) in quantum mechanics in one dimension under the presence of a point singularity. The system considered is the free particle on a line R or on the interval [-l, l] where the point singularity lies at x = 0. In one dimension, the singularity is known to admit a U(2) family of different connection conditions which include as a special case the familiar one that arises under the Dirac delta-potential. Similarly, each of the walls at x = l and x = -l admits a U(1) family of boundary conditions including the Dirichlet and the Neumann boundary conditions. Under these general connection/boundary conditions, the system is shown to possess an N = 1 or N = 2 SUSY for various choices of the singularity and the walls, and the SUSY is found to be `good' or `broken' depending on the choices made. We use the supercharge which allows for a constant shift in the energy, and argue that if the system is supersymmetric then the supercharge is self-adjoint on states that respect the connection/boundary conditions specified by the singularity.
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"abstract": "We study the possibility of supersymmetry (SUSY) in quantum mechanics in one\ndimension under the presence of a point singularity. The system considered is\nthe free particle on a line R or on the interval [-l, l] where the point\nsingularity lies at x = 0. In one dimension, the singularity is known to admit\na U(2) family of different connection conditions which include as a special\ncase the familiar one that arises under the Dirac delta-potential. Similarly,\neach of the walls at x = l and x = -l admits a U(1) family of boundary\nconditions including the Dirichlet and the Neumann boundary conditions. Under\nthese general connection/boundary conditions, the system is shown to possess an\nN = 1 or N = 2 SUSY for various choices of the singularity and the walls, and\nthe SUSY is found to be `good\u0027 or `broken\u0027 depending on the choices made. We\nuse the supercharge which allows for a constant shift in the energy, and argue\nthat if the system is supersymmetric then the supercharge is self-adjoint on\nstates that respect the connection/boundary conditions specified by the\nsingularity.",
"arxiv_id": "quant-ph/0210084",
"authors": [
"Takashi Uchino",
"Izumi Tsutsui"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1016/S0550-3213(03)00352-3",
"journal_ref": "Nucl.Phys.B662:447-460,2003",
"title": "Supersymmetric Quantum Mechanics with a Point Singularity",
"url": "https://arxiv.org/abs/quant-ph/0210084"
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