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

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.

preprint2015arXivOpen access
Rabin BanerjeePradip Mukherjee
hep-thquant-ph
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Rabin BanerjeePradip Mukherjee

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