Hidden symmetry and (super)conformal mechanics in a monopole background

Luis Inzunza (Departamento de Física, Universidad de Santiago de Chile, Casilla, Santiago, 307, Chile; Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, Jena, 07743, Germany) ; Mikhail Plyushchay (Departamento de Física, Universidad de Santiago de Chile, Casilla, Santiago, 307, Chile; Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, Jena, 07743, Germany) ; Andreas Wipf (Departamento de Física, Universidad de Santiago de Chile, Casilla, Santiago, 307, Chile; Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, Jena, 07743, Germany)

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) = 1 2 $$ \frac{1}{2} $$ 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 sop $$ \mathfrak{sop} $$ (2|2) superconformal extension of the system with unbroken N $$ \mathcal{N} $$ = 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).

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      "surname": "Wipf", 
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      "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)."
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Published on:
06 April 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 4
Pages 1-43
DOI:
https://doi.org/10.1007/JHEP04(2020)028
arXiv:
2002.04341
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: