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arXiv · 2111.04014

Construction of a new three boson non-hermitian Hamiltonian associated to deformed Higgs algebra: real eigenvalues and Partial PT-symmetry

Arindam Chakraborty
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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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Arindam Chakraborty. 2021-11-07. Construction of a new three boson non-hermitian Hamiltonian associated to deformed Higgs algebra: real eigenvalues and Partial PT-symmetry. https://arxiv.org/abs/2111.04014

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