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Statistical origin of pseudo-Hermitian supersymmetry and pseudo-hermitian fermions

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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 (nonequivalence) 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 multifermion systems.

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Iop Publishing Ltd

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Physics, multidisciplinary, Physics, mathematical

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Journal of Physics A: Mathematical and General

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10.1088/0305-4470/37/43/012

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