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

Rabin Banerjee, Pradip Mukherjee

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.
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)

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