Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions

Abstract

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N=2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (non-equivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie algebras, and study multi-particle systems of abnormal phermions. The latter provides a certain bosonization of multi-fermion systems.

20 pages, to appear in J.Phys.A

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Cited by in corpus (10)

• Fermionic coherent states for pseudo-Hermitian two-level systems
• Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• Damping and Pseudo-fermions
• Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras
• Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
• Nonlinear n-Pseudo Fermions
• Pseudo-Hermitian systems, involutive symmetries and pseudofermions