A new boson realization of fusion polynomial algebras in non-Hermitian quantum mechanics: γ-deformed su(2) generators, PT -symmetry in Fock space and Higgs algebra

Abstract

Abstract A γ-deformed version of s u ( 2 ) algebra with non-Hermitian generators has been obtained from a bi-orthogonal system of vectors in C 2 . 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 PT -symmetry have been introduced in a typical Fock space setting. The possibility of 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.