Deconstructing non-Dirac-hermitian supersymmetric quantum systems

Abstract

A method to construct non-Dirac-hermitian supersymmetric quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving both bosonic and fermionic degrees of freedom in terms of non-Dirac-hermitian operators which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. A pseudo-hermitian realization of the Clifford algebra for a pre-determined positive-definite metric is used to construct supersymmetric systems with one or many degrees of freedom. It is shown that exactly solvable non-Dirac-hermitian supersymmetric quantum systems can be constructed corresponding to each exactly solvable Dirac-hermitian system. Examples of non-Dirac-hermitian (i) non-relativistic Pauli Hamiltonian, (ii) super-conformal quantum system and (iii) supersymmetric Calogero-type models admitting entirely real spectra are presented.

27 pages, LateX, no figures

References in corpus (8)

• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Exactly Solvable Quasi-hermitian Transverse Ising Model
• Level statistics of a pseudo-Hermitian Dicke model
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• PT-symmetric deformations of Calogero models
• Quantum Phase Transition in a Pseudo-hermitian Dicke model
• From real fields to complex Calogero particles
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations