Hidden superconformal symmetry: Where does it come from?

It is known that a single quantum harmonic oscillator is characterized by a hidden spectrum generating superconformal symmetry, but its origin has remained rather obscure. We show how this hidden superconformal symmetry can be derived by applying a nonlocal Foldy-Wouthuysen transformation to three e...

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Bibliographic Details
Published in:Physical review. D 2018-02, Vol.97 (4), Article 045002
Main Authors: Inzunza, Luis, Plyushchay, Mikhail S.
Format: Article
Language:English
Subjects:
Harmonic oscillators
Quantum mechanics
Quantum theory
Supersymmetry
Symmetry
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Summary:It is known that a single quantum harmonic oscillator is characterized by a hidden spectrum generating superconformal symmetry, but its origin has remained rather obscure. We show how this hidden superconformal symmetry can be derived by applying a nonlocal Foldy-Wouthuysen transformation to three extended systems with fermion degrees of freedom. The associated systems have essentially different nature from the point of view of conventional supersymmetric quantum mechanics, and generate the desired hidden symmetry in three different ways. We also trace out how the hidden superconformal symmetry of the quantum free particle system is produced in the limit of zero frequency.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.97.045002