On the representation theory of orthofermions and orthosupersymmetric realization of parasupersymmetry and fractional supersymmetry

Mostafazadeh, Alí

doi:10.1088/0305-4470/34/41/315

Cited by 11 publications

(21 citation statements)

References 16 publications

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“…For instance, according to Ref. [15] every orthosupersymmetric system [16] admits both parasupersymmetry and fractional supersymmetry [17]. Combining this fact with the present results shown in this letter, we conjecture the existence of 'N -fold generalization' of other supersymmetric variants such as N -fold fractional supersymmetry characterized by the following non-linear relation …”

Section: An Examplesupporting

confidence: 79%

$\mathcal{N}$-FOLD PARASUPERSYMMETRY

Tanaka

2007

Mod. Phys. Lett. A

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We find a new type of non-linear supersymmetries, called N -fold parasupersymmetry, which is a generalization of both N -fold supersymmetry and parasupersymmetry. We provide a general formulation of this new symmetry and then construct a second-order N -fold parasupersymmetric quantum system where all the components of N -fold parasupercharges are given by type A N -fold supercharges. We show that this system exactly reduces to the Rubakov-Spiridonov model when N = 1 and admits a generalized type C 2N -fold superalgebra. We conjecture the existence of other 'N -fold generalizations' such as N -fold fractional supersymmetry, N -fold orthosupersymmetry, and so on.

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Section: An Examplesupporting

confidence: 79%

$\mathcal{N}$-FOLD PARASUPERSYMMETRY

Tanaka

2007

Mod. Phys. Lett. A

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“…The similarity between the algebraic structure of supersymmetry and pseudo-supersymmetry suggests various generalizations of the latter. For example, one may examine para-, ortho-, and fractional pseudo-supersymmetry whose algebras are respectively obtained by replacing the adjoint of the operators by their pseudo-adjoint in the algebras of parasupersymmetry, orthosupersymmetry, and fractional supersymmetry, [18,29]. More generally, it would be interesting to generalize the concept of a topological symmetry [19] to quantum systems with a pseudo-Hermitian Hamiltonian.…”

Section: Resultsmentioning

confidence: 99%

Pseudo-supersymmetric quantum mechanics and isospectral pseudo-Hermitian Hamiltonians

2002

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We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily Hermitian) Hamiltonians with discrete spectra and real or complex-conjugate pairs of eigenvalues are isospectral and have identical degeneracy structure except perhaps for the zero eigenvalue if and only if they are pseudo-supersymmetric partners. This implies that pseudo-supersymmetry is the basic framework for generating non-Hermitian P T -symmetric and non-P T -symmetric Hamiltonians with a real spectrum via a Darboux transformation, and shows that every diagonalizable Hamiltonian H with a discrete spectrum and real or complex-conjugate pairs of eigenvalues may be factored as H = L ♯ L where L is a linear operator with pseudo-adjoint L ♯ . In particular, this factorization applies to P T -symmetric and Hermitian Hamiltonians. The nondegenerate two-level systems provide a class of Hamiltonians that are pseudo-Hermitian. We demonstrate the implications of our general results for this class in some detail.

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“…Multi abnormal phermionic versus parafermionic systems: One can use the physical creation and annihilation operators for multi abnormal phermionic systems to obtain a realization of those of a parafermionic system of appropriate order. This may be viewed as an alternative to the Green's ansatz [47,31] and orthofermionic [10,18] constructions of the latter. It may also provide means to describe the hidden supersymmetries of the corresponding parafermionic systems [48] and investigate their analogs for general multi abnormal phermionic systems.…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, the irreducible * -representations of this algebra does not support an indefinite 9 This may be established using the approach of [10].…”

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confidence: 99%

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

Mostafazadeh¹

2004

J. Phys. A: Math. Gen.

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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 pseudoHermitian 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 bosonabnormal-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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On the representation theory of orthofermions and orthosupersymmetric realization of parasupersymmetry and fractional supersymmetry

Cited by 11 publications

References 16 publications

$\mathcal{N}$-FOLD PARASUPERSYMMETRY

$\mathcal{N}$-FOLD PARASUPERSYMMETRY

Pseudo-supersymmetric quantum mechanics and isospectral pseudo-Hermitian Hamiltonians

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

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