We study classical and quantum hidden symmetries of a particle with electric charge e in the background of a Dirac monopole of magnetic charge g subjected to an additional central potential V (r) = U (r) + (eg)2 /2mr 2 with U (r) = $$ \frac{1}{2} $$ mω 2 r 2, similar to that in the one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF). By means of a non-unitary conformal bridge transformation, we establish a relation of the quantum states and of all symmetries of the system with those of the system without harmonic trap, U (r) = 0. Introducing spin degrees of freedom via a very special spin-orbit coupling, we construct the $$ \mathfrak{sop} $$ (2|2) superconformal extension of the system with unbroken $$ \mathcal{N} $$ = 2 Poincaré supersymmetry and show that two different superconformal extensions of the one-dimensional AFF model with unbroken and spontaneously broken supersymmetry have a common origin. We also show a universal relationship between the dynamics of a Euclidean particle in an arbitrary central potential U (r) and the dynamics of a charged particle in a monopole background subjected to the potential V (r).
{ "_oai": { "updated": "2020-04-06T18:33:00Z", "id": "oai:repo.scoap3.org:53686", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Chile", "value": "Departamento de F\u00edsica, Universidad de Santiago de Chile, Casilla, Santiago, 307, Chile", "organization": "Universidad de Santiago de Chile" }, { "country": "Germany", "value": "Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, Max-Wien-Platz 1, Jena, 07743, Germany", "organization": "Friedrich-Schiller-Universit\u00e4t Jena" } ], "surname": "Inzunza", "email": "luis.inzunza@usach.cl", "full_name": "Inzunza, Luis", "given_names": "Luis" }, { "affiliations": [ { "country": "Chile", "value": "Departamento de F\u00edsica, Universidad de Santiago de Chile, Casilla, Santiago, 307, Chile", "organization": "Universidad de Santiago de Chile" }, { "country": "Germany", "value": "Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, Max-Wien-Platz 1, Jena, 07743, Germany", "organization": "Friedrich-Schiller-Universit\u00e4t Jena" } ], "surname": "Plyushchay", "email": "mikhail.plyushchay@usach.cl", "full_name": "Plyushchay, Mikhail", "given_names": "Mikhail" }, { "affiliations": [ { "country": "Chile", "value": "Departamento de F\u00edsica, Universidad de Santiago de Chile, Casilla, Santiago, 307, Chile", "organization": "Universidad de Santiago de Chile" }, { "country": "Germany", "value": "Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, Max-Wien-Platz 1, Jena, 07743, Germany", "organization": "Friedrich-Schiller-Universit\u00e4t Jena" } ], "surname": "Wipf", "email": "wipf@tpi.uni-jena.de", "full_name": "Wipf, Andreas", "given_names": "Andreas" } ], "titles": [ { "source": "Springer", "title": "Hidden symmetry and (super)conformal mechanics in a monopole background" } ], "dois": [ { "value": "10.1007/JHEP04(2020)028" } ], "publication_info": [ { "page_end": "43", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2020", "artid": "JHEP04(2020)028", "year": 2020, "page_start": "1", "journal_issue": "4" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2020-04-06T20:30:29.666445", "source": "Springer", "method": "Springer", "submission_number": "9fcd7732783411ea832002163e01809a" }, "page_nr": [ 43 ], "license": [ { "url": "https://creativecommons.org/licenses/by/3.0", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2020" } ], "control_number": "53686", "record_creation_date": "2020-04-06T20:30:29.666476", "_files": [ { "checksum": "md5:46142d4c25be8386d0f3f90763157db1", "filetype": "xml", "bucket": "d53387e2-48e2-4ec8-bee8-0b74e416ba94", "version_id": "64e0ff10-cb0f-43bf-a137-aaa42d549575", "key": "10.1007/JHEP04(2020)028.xml", "size": 13109 }, { "checksum": "md5:7cae06c10c124ce71e44aa2fd4dc7dde", "filetype": "pdf/a", "bucket": "d53387e2-48e2-4ec8-bee8-0b74e416ba94", "version_id": "fb7cc915-e3d5-4ce6-bb29-ea2d3b5ff097", "key": "10.1007/JHEP04(2020)028_a.pdf", "size": 1383001 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th" ], "value": "2002.04341" } ], "abstracts": [ { "source": "Springer", "value": "We study classical and quantum hidden symmetries of a particle with electric charge e in the background of a Dirac monopole of magnetic charge g subjected to an additional central potential V (r) = U (r) + (eg)2 /2mr 2 with U (r) = <math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math> $$ \\frac{1}{2} $$ m\u03c9 2 r 2, similar to that in the one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF). By means of a non-unitary conformal bridge transformation, we establish a relation of the quantum states and of all symmetries of the system with those of the system without harmonic trap, U (r) = 0. Introducing spin degrees of freedom via a very special spin-orbit coupling, we construct the <math> <mi>sop</mi> </math> $$ \\mathfrak{sop} $$ (2|2) superconformal extension of the system with unbroken <math> <mi>N</mi> </math> $$ \\mathcal{N} $$ = 2 Poincar\u00e9 supersymmetry and show that two different superconformal extensions of the one-dimensional AFF model with unbroken and spontaneously broken supersymmetry have a common origin. We also show a universal relationship between the dynamics of a Euclidean particle in an arbitrary central potential U (r) and the dynamics of a charged particle in a monopole background subjected to the potential V (r)." } ], "imprints": [ { "date": "2020-04-06", "publisher": "Springer" } ] }