A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : γ-deformed su(2) generators, Partial PT -symmetry and Higgs algebra

Abstract

A γ-deformed version of $\mathfrak{s}\mathfrak{u}\left(2\right)$ algebra with non-Hermitian generators has been obtained from a bi-orthogonal system of vectors in C2. The related Jordan–Schwinger map is combined with boson algebras to obtain a hierarchy of fusion polynomial algebras. This makes possible the construction of Higgs algebra of cubic polynomial type which eventually leads to several multi-boson non-Hermitian Hamiltonians. Finally, the notion of global and partial $\mathcal{PT}$-symmetry have been introduced in a typical Fock space setting. 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. The symmetry behavior has been conceptualized in terms of a couple of toy models.