Anyonic realization of the quantum affine Lie algebra

Frappat, L.; Sciarrino, A.; Sciuto, S.; Sorba, P.

doi:10.1016/0370-2693(95)01518-3

Cited by 14 publications

(14 citation statements)

References 10 publications

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“…The subject of anyons has been well investigated in the literature, especially in the context of quantum field theory and the braid group [2,5,7,8]. Interesting results have also been derived to describe the thermostatistics of anyons, such as determining the virial coefficients [11,13].…”

Section: Introductionmentioning

confidence: 99%

“…Although the algebra of q-oscillators appears in the literature on the subject of anyons [7,8,20], it is also known that q-oscillators may have nothing to do with anyons since the former exist in arbitrary space-time dimensions. In our formulation, we do not use q-oscillator algebra, neither do we use Fock states.…”

Section: The Distribution Functionmentioning

confidence: 99%

“…The objects named anyons [1][2][3][4][5][6][7][8] carry both an electric charge and a magnetic flux. They have attracted a great deal of attention and have been the subject of intense investigation in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Detailed balance and intermediate statistics

Acharya

Swamy

2004

J. Phys. A: Math. Gen.

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We present a theory of particles, obeying intermediate statistics ("anyons"), interpolating between Bosons and Fermions, based on the principle of Detailed Balance. It is demonstrated that the scattering probabilities of identical particles can be expressed in terms of the basic numbers, which arise naturally and logically in this theory. A transcendental equation determining the distribution function of anyons is obtained in terms of the statistics parameter, whose limiting values 0 and 1 correspond to Bosons and Fermions respectively. The distribution function is determined as a power series involving the Boltzmann factor and the statistics parameter and we also express the distribution function as an infinite continued fraction. The last form enables one to develop approximate forms for the distribution function, with the first approximant agreeing with our earlier investigation.

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Section: Introductionmentioning

confidence: 99%

Section: The Distribution Functionmentioning

confidence: 99%

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Detailed balance and intermediate statistics

Acharya

Swamy

2004

J. Phys. A: Math. Gen.

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“…Let us mention that anyon systems have also been considered in the discrete setting, i.e., when T ⊂ N, see e.g. [12,23,13]. It should be, however, mentioned that, when discussing the anyons in the discete setting, Goldin and Majid [13] dropped the assumption that the annihilation operator is adjoint of the creation operator, and proved an anyonic exclusion principle for their model.…”

Section: Introductionmentioning

confidence: 99%

Fock representations of Q-deformed commutation relations

Bożejko

Lytvynov

Wysoczański

2017

Journal of Mathematical Physics

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We consider Fock representations of the Q-deformed commutation relationsHere T := R d (or more generally T is a locally compact Polish space), the function Q : T 2 → C satisfies |Q(s, t)| ≤ 1 and Q(s, t) = Q(t, s), andσ being a fixed reference measure on T . In the case where |Q(s, t)| ≡ 1, the Q-deformed commutation relations describe a generalized statistics studied by Liguori and Mintchev (1995). These generalized statistics contain anyon statistics as a special case (with T = R 2 and a special choice of the function Q). The related Q-deformed Fock space F(H) over H := L 2 (T → C, σ) is constructed. An explicit form of the orthogonal projection of H ⊗n onto the n-particle space F n (H) is derived. A scalar product in F n (H) is given by an operator P n ≥ 0 in H ⊗n which is strictly positive on F n (H). We realize the smeared operators ∂ † t and ∂ t as creation and annihilation operators in F(H), respectively. Additional Q-commutation relations are obtained between the creation operators and between the annihilation operators. They are of the form ∂ † s ∂ † t = Q(t, s)∂ † t ∂ † s , ∂ s ∂ t = Q(t, s)∂ t ∂ s , valid for those s, t ∈ T for which |Q(s, t)| = 1.

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“…While this picture relating 2 + 1 and 1 + 1 physics, which we briefly sketched, has been greatly developed and clarified, new ideas have emerged in 1 + 1 dimensions whose corresponding rôle (if any) in 2 + 1 dimensions remains unclear. In this regard, q-deformed affine Lie algebras associated with quantum groups [12] have been formulated for the entire non-exceptional series and a construction in terms of anyonic q-deformed oscillators has been given, at least for the unitary and symplectic cases [13]. Furthermore, q-deformed affine Lie algebras, enter in different aspects of 1 + 1 integrable models [14,15].…”

Section: Introductionmentioning

confidence: 99%

Deformed Chern-Simons theories

et al. 1997

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We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field strengths become q-commuting fields. Our approach, which is explicitly carried out for the case of 'minimal' deformations, has the advantage of leading naturally to a consistent Hamiltonian structure that has essentially all of the features of the undeformed case. For example, using the new Poisson brackets, the constraints form a closed algebra and generate q-deformed gauge transformations. DSF 16/97UAHEP 975

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Anyonic realization of the quantum affine Lie algebra

Cited by 14 publications

References 10 publications

Detailed balance and intermediate statistics

Detailed balance and intermediate statistics

Fock representations of Q-deformed commutation relations

Deformed Chern-Simons theories

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