$PT$ symmetry and a dynamical realization of the SU(1,1) algebra
Quantum Physics
2015-03-24 v2 High Energy Physics - Theory
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.
Keywords
Cite
@article{arxiv.1410.4678,
title = {$PT$ symmetry and a dynamical realization of the SU(1,1) algebra},
author = {Rabin Banerjee and Pradip Mukherjee},
journal= {arXiv preprint arXiv:1410.4678},
year = {2015}
}
Comments
13 pages. enlarged version explaining quantization procedure