On Some novel features of a Non-Hermitian multi-boson Hamiltonian : partial PL -symmetry and ghosts

Abstract

The eigenvalues and eigenstates of a three-boson Hamiltonian are considered. The Hamiltonian is found to be pseudo-Hermitian in relation to its various partial PT-symmetries understood in a Fock space setting. The possibilities of symmetry adopting and symmetry breaking states are also discussed. Ghost states are found in relation to different symmetry induced inner-products. At least two of the ghost states show some kind of transition to normal states depending on the values of certain parameter.