The origin of the hidden supersymmetry
Vit Jakubsky, Luis-Miguel Nieto, Mikhail S. Plyushchay
TL;DR
This paper explains the origin of hidden supersymmetry in various quantum systems using a nonlocal unitary transformation, revealing new insights into bosonized supersymmetry and superconformal symmetry.
Contribution
It introduces a unified explanation for hidden supersymmetry and superconformal symmetry in quantum systems via a special nonlocal transformation, extending understanding of N=2 supersymmetry.
Findings
Hidden supersymmetry explained by nonlocal transformation
Bosonized supersymmetry emerges in parity even systems
Unusual N=2 supersymmetry of electrons in magnetic fields clarified
Abstract
The hidden supersymmetry and related tri-supersymmetric structure of the free particle system, the Dirac delta potential problem and the Aharonov-Bohm effect (planar, bound state, and tubule models) are explained by a special nonlocal unitary transformation, which for the usual N=2 supercharges has a nature of Foldy-Wouthuysen transformation. We show that in general case, the bosonized supersymmetry of nonlocal, parity even systems emerges in the same construction, and explain the origin of the unusual N=2 supersymmetry of electron in three-dimensional parity even magnetic field. The observation extends to include the hidden superconformal symmetry.
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