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arXiv · 1410.4678

$PT$ symmetry and a dynamical realization of the SU(1,1) algebra

Rabin Banerjee·Pradip Mukherjee
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Abstract

We show that the elementary modes of the planar harmonic oscillator can be quantised in the framework of quantum mechanics based on pseudo-hermitian hamiltonians. These quantised modes are demonstrated to act as dynamical structures behind a new Jordan - Schwinger realization of the SU(1,1) algebra. This analysis complements the conventional Jordan - Schwinger construction of the SU(2) algebra based on hermitian hamiltonians of a doublet of oscillators.

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Rabin Banerjee, Pradip Mukherjee. 2015-03-23. $PT$ symmetry and a dynamical realization of the SU(1,1) algebra. https://arxiv.org/abs/1410.4678

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