New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra

Abstract

The recently introduced two- and three-parameter ($p,q$)- and ($p,q,\mu$)-deformed extensions of the Heisenberg algebra were explored under the condition of their connectedness with the respective nonstandard (other than known ones) deformed quantum oscillator algebras. In this paper we show that such connection dictates certain new $\eta (N)$-pseudo-Hermitian conjugation rule between the creation and annihilation operators, with $\eta (N)$ depending on the particle number operator $N$. In turn, that leads to the related $\eta (N)$-pseudo-Hermiticity of the position/momentum operators, though the involved Hamiltonian is Hermitian. Different possible cases are studied, and some interesting features implied by the use of such $\eta (N)$-based conjugation rule are emphasized.

v2: 15 pages, clarifying text added in sec.3, title slightly changed, matches published version

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Interactions of Hermitian and non-Hermitian Hamiltonians
• Correlation function intercepts for $\tilde{\mu },q$-deformed Bose gas model implying effective accounting for interaction and compositeness of particles
• Energy dependence of the entanglement entropy of composite boson (quasiboson) systems
• Three-parameter (two-sided) deformation of Heisenberg algebra

Cited by in corpus (4)

• Time correlation functions and Fisher zeros for q-deformed Bose gas
• Nonstandard Deformed Oscillators from $q$- and $p,q$-Deformations of Heisenberg Algebra
• New Deformed Heisenberg Algebra from the $\mu$-Deformed Model of Dark Matter
• Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators