Unitary and pseudounitary symmetries in a generalized statistics

Falco, L. De; Mignani, Roberto; Scipioni, Roberto

doi:10.1016/0375-9601(95)00220-w

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…It is clear that one can recover the results obtained in (De Falco et al, 1995) and (De Falco and Mignani, 1996) from our construction, in the particular case l = 2 (ct = 0, 1). The algebra generated by ao, a~, and No is bosonic:…”

Section: Ot -1) the Fock Space Fo Is Infinite-dimensional (Bosonicsupporting

confidence: 62%

“…This is the result obtained in (De Falco et al, 1995;De Falco and Mignani, 1996) corresponding to the Fock-like space F = F1 9 F0, which we call the fermionic realization.…”

Section: Ot -1) the Fock Space Fo Is Infinite-dimensional (Bosonicmentioning

confidence: 63%

“…A possibility to shed some light on caracteristic symmetries of these particular systems of particles involves quantum groups which are deformations of ordinary Lie algebras. It has been shown (Biedenham, 1989; Macfarlane, 1989) that the realization of these mathematical objects can be obtained by using some consistent q-deformation of the oscillator algebras.Recently, it was remarked (De Falco et al, 1995; De Falco and Mignani, 1996) that the deformed Heisenberg-Weyl (HW) algebra appears in the intermediate statistics. To realize this (HW) algebra the authors consider some deformation matrix G instead of just a deformation parameter q.…”

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confidence: 98%

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Quonic realization of the deformed Heisenberg-Weyl algebra

1997

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A consistent realization of an operatorial deformed Heisenberg-Weyl (HW) algebra is given. The explicit construction of the deformation matrix is discussed. The corresponding generalized Fock-like space is analyzed.In the last few years, great interest has been devoted to the study and the understanding of intermediate statistics, also called exotic statistics (Leineas and Myrheim, 1977). The latter describe particles interpolating between bosons and fermions and are characterized by a fractional spin or more generally by fractional quantum numbers. These exotic particles appear in the study of the fractional quantum Hall effect and in the theory of high-temperature superconductivity (Halperin, 1984;Chen et al., 1989). A possibility to shed some light on caracteristic symmetries of these particular systems of particles involves quantum groups which are deformations of ordinary Lie algebras. It has been shown (Biedenham, 1989; Macfarlane, 1989) that the realization of these mathematical objects can be obtained by using some consistent q-deformation of the oscillator algebras.Recently, it was remarked (De Falco et al., 1995; De Falco and Mignani, 1996) that the deformed Heisenberg-Weyl (HW) algebra appears in the intermediate statistics. To realize this (HW) algebra the authors consider some deformation matrix G instead of just a deformation parameter q.Indeed, an explicit calculus concerning a bosonic and a fermionic evendimensional realization of an operatorial deformation of the HW algebra has been performed. In the present work, we give a generalization of this study, and by using a mathematical framework of quonic algebra, we obtain a i Laboratoire de Physique Throrique (LPT-ICAC), Facult6 des Sciences, Universit6 Mohamed V, Rabat, Morocco.

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Section: Ot -1) the Fock Space Fo Is Infinite-dimensional (Bosonicsupporting

confidence: 62%

“…This is the result obtained in (De Falco et al, 1995;De Falco and Mignani, 1996) corresponding to the Fock-like space F = F1 9 F0, which we call the fermionic realization.…”

Section: Ot -1) the Fock Space Fo Is Infinite-dimensional (Bosonicmentioning

confidence: 63%

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confidence: 98%

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Quonic realization of the deformed Heisenberg-Weyl algebra

1997

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“…About 20 years ago, the generalization of the fermion algebra was proposed by some authors: [4][5][6][7][8] …”

Section: W S Chungmentioning

confidence: 99%

Polynomial algebra with reflection symmetry and thermostatistics

Chung

2015

Mod. Phys. Lett. A

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In this paper, we use the reflection (or parity) operator to construct the new algebra whose maximum occupation number is finite. For the Hamiltonian proportional to the number operator, we discuss the thermostatistics and compute the thermodynamical quantities such as distribution function, multiparticle distribution function, mean energy and specific heat. We also calculate the intercept for this algebra to show that a particle obeying this algebra is an exotic particle which is neither a boson nor a fermion.

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“…At least within this representation it is rather likely that the form introduced by McDermott and Solomon [5] is sufficiently general. The non-degeneracy requirement of the ground state has recently been relaxed by several authors [16][17][18] who introduced a doubly-degenerate ground state that was found useful in the context of discussing intermediate statistics. We shall not pursue this extension.…”

Section: Equivalence Of Quommutators and Commutatorsmentioning

confidence: 99%

Recursively minimally-deformed oscillators

Katriel

Quesne

1996

Journal of Mathematical Physics

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A recursive deformation of the boson commutation relation is introduced. Each step consists of a minimal deformation of a commutator [a, a † ] = f k (· · · ;n) into [a, a † ] q k+1 = f k (· · · ;n), where · · · stands for the set of deformation parameters that f k depends on, followed by a transformation into the commutator [a, a † ] = f k+1 (· · · , q k+1 ;n) to which the deformed commutator is equivalent within the Fock space. Starting from the harmonic oscillator commutation relation [a, a † ] = 1 we obtain the Arik-Coon and the Macfarlane-Biedenharn oscillators at the first and second steps, respectively, followed by a sequence of multiparameter generalizations. Several other types of deformed commutation relations related to the treatment of integrable models and to parastatistics are also obtained. The "generic" form consists of a linear combination of exponentials of the number operator, and the various recursive families can be classified according to the number of free linear parameters involved, that depends on the form of the initial commutator.

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Unitary and pseudounitary symmetries in a generalized statistics

Cited by 5 publications

References 9 publications

Quonic realization of the deformed Heisenberg-Weyl algebra

Quonic realization of the deformed Heisenberg-Weyl algebra

Polynomial algebra with reflection symmetry and thermostatistics

Recursively minimally-deformed oscillators

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