Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems

Abstract

A method to construct non-dissipative non-Dirac-hermitian relativistic 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 the Dirac matrices and the bosonic 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. Several examples of exactly solvable non-dissipative non-Dirac-hermitian relativistic quantum systems are presented by establishing/employing a connection between Dirac equation and supersymmetry

11 pages, LaTeX, no figures

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• On regular and chaotic dynamics of a non-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions