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Email: mphys11@ipb.ac.rs

Abstracts
Todor Popov
Dynamical supersymmetry of the Landau levels
The Landau problem and harmonic oscillator in the plane share a Hilbert space that carries the structure of Dirac's remarkable so(2,3) representation. We show that the orthosymplectic algebra osp(14) is the spectrumgenerating algebra for the Landau problem and, hence, for the 2D isotropic harmonic oscillator. This algebra generates a stack of Bargmann spaces in onetoone correspondence with the Landau levels. The 2D harmonic oscillator is in duality with the 2D quantum CoulombKepler systems, with the osp(14) symmetry broken down to the conformal symmetry so(2,3). The even so(2,3) submodule (coined Rac) generated from the ground state of zero angular momentum is identified with the Hilbert space of a 2D hydrogen atom. An odd element of the superalgebra osp(14) creates a pseudovacuum with intrinsic angular momentum 1/2 from the vacuum. The odd so(2,3)submodule (coined Di) built upon the pseudovacuum is the Hilbert space of a magnetized 2D hydrogen atom: a quantum system of a dyon and an electron. Thus, the Hilbert space of the Landau problem is a direct sum of two massless unitary so(2,3) representations, namely, the Di and Rac singletons introduced by Flato and Fronsdal.


Organizer:
Institute of Physics Belgrade (University of Belgrade)
Belgrade, Serbia
Coorganizers:
Faculty of Mathematics
(University of Belgrade)
Belgrade, Serbia
Mathematical Institute
(Serbian Academy of Sciences and Arts)
Belgrade, Serbia
Serbian Academy of Nonlinear Sciences (SANS)
Belgrade, Serbia
ZOOM link for attending lectures online:
https://us06web.zoom.us/j/81395737972?pwd=kZEEjWagmat78h2FHLb4TMCsdM7ZF3.1
Meeting ID: 813 9573 7972
Passcode: 824870
