Department of Mathematics2024-11-1020040305-447010.1088/0305-4470/37/43/0122-s2.0-8744291868http://dx.doi.org/10.1088/0305-4470/37/43/012https://hdl.handle.net/20.500.14288/17415We 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.Physics, multidisciplinaryPhysics, mathematicalConference proceeding225151100013Q213002