English

$PT$ 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