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

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

2004-04-05

arxiv.org/abs/quant-ph/0404025v1

J.Phys.A37:10193-10208,2004

Physics

Quantum Physics

20 pages, to appear in J.Phys.A

Scientific paper

10.1088/0305-4470/37/43/012

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.

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