Construction of a new three boson non-hermitian Hamiltonian associated
to deformed Higgs algebra: real eigenvalues and Partial PT-symmetry
- URL: http://arxiv.org/abs/2111.04014v1
- Date: Sun, 7 Nov 2021 06:40:47 GMT
- Title: Construction of a new three boson non-hermitian Hamiltonian associated
to deformed Higgs algebra: real eigenvalues and Partial PT-symmetry
- Authors: Arindam Chakraborty
- Abstract summary: Fusion of Jordan-Schwinger realization of complexified $mathfraksu(2)$ with Dyson-Maleev representation.
Non-hermitian Hamiltonian has real eigenvalues and eigensymmetry inducedity.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A $\gamma$-deformed version of $\mathfrak{su}(2)$ algebra has been obtained
from a bi-orthogonal system of vectors in $\bf{C^2}$. Fusion of
Jordan-Schwinger realization of complexified $\mathfrak{su}(2)$ with
Dyson-Maleev representation gives a 3-boson realization of Higgs algebra of
cubic polynomial type. The non-hermitian Hamiltonian thus obtained is found to
have real eigenvalues and eigen states with symmetry induced orthogonality. The
notion of partial ${\mathcal {PT}}$-symmetry (henceforth $\partial_{\mathcal {
PT}}$) has been introduced as a characteristic feature of these multi-boson
realizations. The Hamiltonian along with its eigenstates have been studied in
the light of $\partial_{\mathcal { PT}}$-symmetry. The possibility of
$\partial_{\mathcal { PT}}$-symmetry breaking is also discussed. The
deformation parameter $\gamma$ plays a crucial role in the entire formulation
and non-trivially modifies the eigenfunctions under consideration.
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