$PT$ symmetry and a dynamical realization of the SU(1,1) algebra
Rabin Banerjee, Pradip Mukherjee
TL;DR
This paper demonstrates that elementary modes of the planar harmonic oscillator can be quantized using pseudo-Hermitian Hamiltonians, leading to a new dynamical realization of the SU(1,1) algebra that complements the traditional SU(2) construction.
Contribution
It introduces a novel Jordan-Schwinger realization of SU(1,1) algebra based on pseudo-Hermitian quantization of planar harmonic oscillator modes.
Findings
Pseudo-Hermitian Hamiltonians enable quantization of planar harmonic oscillator modes.
New SU(1,1) algebra realization derived from these modes.
Complementary to the conventional SU(2) algebra construction.
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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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Mechanical and Optical Resonators · Orbital Angular Momentum in Optics