A q-analogue of the supersymmetric oscillator and its q-superalgebra

Parthasarathy, R.; Viswanathan, K. S.

doi:10.1088/0305-4470/24/3/019

Cited by 89 publications

(85 citation statements)

References 7 publications

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“…There are considerations of q-deformed coherent states on quantum algebras, in particular on the q-deformation of the universal enveloping U q (su (2)), see [28]- [31], [36]- [38]. Because of the duality between the quantum groups and the quantum algebra it is possible that there is a relation between our coherent states and the coherent states on quantum algebras.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…q-deformed coherent states were considered in [28]- [31]. Coherent states on classical Lie groups are defined as [27],…”

Section: Introductionmentioning

confidence: 99%

“…We are not discussing here coherent states on the q-deformed universal enveloping algebras [34,35], [28]- [31], [36]- [38]. We hope to clarify a relation of these with (1) and (2) in a forthcoming publication.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coherent States, Dynamics and Semiclassical Limit on Quantum Groups

Aref’eva¹,

Parthasarathy²,

Viswanathan³

et al. 1994

Mod. Phys. Lett. A

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Coherent states on the quantum group SU q (2) are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit q → 1 is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to q-deformation as a q-Weyl quantization and a relavence of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…q-deformed coherent states were considered in [28]- [31]. Coherent states on classical Lie groups are defined as [27],…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coherent States, Dynamics and Semiclassical Limit on Quantum Groups

Aref’eva¹,

Parthasarathy²,

Viswanathan³

et al. 1994

Mod. Phys. Lett. A

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“…This allows us to identify the boson and fermion algebras with (15) and (18) respectively. Now, consider the boson-fermion oscillator [34] whose Hamiltonian is given by (3) with E > 0, N denoting the boson number operator (16), and N labelling the fermion number operator (19).…”

Section: Algebras Of Creation and Annihilation Operators And The Basimentioning

confidence: 99%

“…The q-boson-fermion and q-boson-q-fermion exchange symmetries have also been considered in the literature [14,15].…”

mentioning

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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(p, q)-Rogers-Szegö Polynomial and the (p, q)-Oscillator

Jagannathan

Sridhar²

2010

The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

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A q-analogue of the supersymmetric oscillator and its q-superalgebra

Cited by 89 publications

References 7 publications

Coherent States, Dynamics and Semiclassical Limit on Quantum Groups

Coherent States, Dynamics and Semiclassical Limit on Quantum Groups

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

(p, q)-Rogers-Szegö Polynomial and the (p, q)-Oscillator

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