2021/11/07 by Chakraborty, Arindam
#FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum theory
paper · doi:10.48550/arxiv.2111.04014
A γ-deformed version of \mathfraksu(2) algebra has been obtained from a bi-orthogonal system of vectors in \bfC2. Fusion of Jordan-Schwinger realization of complexified \mathfraksu(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 ∂_\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 ∂_\mathcal PT-symmetry. The possibility of ∂_\mathcal PT-symmetry breaking is also discussed. The deformation parameter γ plays a crucial role in the entire formulation and non-trivially modifies the eigenfunctions under consideration.