On Some novel features of a Non-Hermitian multi-boson Hamiltonian : partial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:math> -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.