Calogero-Moser Models with Noncommutative Spin Interactions

Polychronakos, Alexios P.

doi:10.1103/physrevlett.89.126403

Cited by 20 publications

(18 citation statements)

References 44 publications

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“…This case surprisingly yields U(2)-spin Calogero system [17,18] in the bosonic sector. The most natural formulation of N =4, d=1 models is achieved in the harmonic superspace [19,20] parametrized by the coordinates (t, θ i , θk , u ± i ), i, k = 1, 2, where commuting mutually conjugate SU(2)doublets u ± i are harmonic coordinates, u +i u − i = 1.…”

Section: N =4 Supersymmetric Extensionmentioning

confidence: 93%

“…gauge connections entering the spinor covariant derivatives in (18) are properly expressed through V ++ (ζ, u) [12]. The parameters of the U(n) gauge group are analytic, so…”

Section: N =4 Supersymmetric Extensionmentioning

confidence: 99%

“…Our approach is a minimal superfield generalization of this bosonic U(n) gauging. Requiring the supersymmetric gauge models to possess N -extended superconformal symmetry essentially constrains the structure of the corresponding actions and allows one to reveal, in their bosonic sector, either the standard Calogero model (4) (in the cases of N =1 and N =2) or the U(2)-spin Calogero model [3,17,18] modified by a conformal potential for the center-of-mass coordinate (in the N =4 case). In this short note we outline the basic features of our construction, leaving details, quantization and comparison with the previously known superextended Calogero models for a longer paper.…”

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confidence: 99%

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Supersymmetric Calogero models by gauging

Fedoruk¹,

Ivanov²,

Lechtenfeld

2009

Phys. Rev. D

189

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New superconformal extensions of d=1 Calogero-type systems are obtained by gauging the U(n) isometry of matrix superfield models. We consider the cases of N=1, N=2 and N=4 one-dimensional supersymmetries. The bosonic core of the N=1 and N=2 models is the standard conformal A_{n-1} Calogero system, whereas the N=4 model is an extension of the U(2)-spin Calogero system.Comment: 5 pages; v2: minor clarifications, refs. added, version published in PR

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Section: N =4 Supersymmetric Extensionmentioning

confidence: 93%

“…gauge connections entering the spinor covariant derivatives in (18) are properly expressed through V ++ (ζ, u) [12]. The parameters of the U(n) gauge group are analytic, so…”

Section: N =4 Supersymmetric Extensionmentioning

confidence: 99%

mentioning

confidence: 99%

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Supersymmetric Calogero models by gauging

Fedoruk¹,

Ivanov²,

Lechtenfeld

2009

Phys. Rev. D

189

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“…(Further generalizations of these models involving a "twisted" symmetry element were found in [24].) In principle our models with dihedral symmetry could also be obtained by reductions of rational models involving parity in addition to translation symmetry, though this has not been done explicitly.…”

Section: Discussionmentioning

confidence: 99%

Sutherland models for complex reflection groups

Crampé¹,

Young²

2008

Nuclear Physics B

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There are known to be integrable Sutherland models associated to every real root system -or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper we associate certain integrable Sutherland models to the classical family of complex reflection groups. Internal degrees of freedom are introduced, defining dynamical spin chains, and the freezing limit taken to obtain static chains of Haldane-Shastry type. By considering the relation of these models to the usual BC N case, we are led to systems with both real and complex reflection groups as symmetries. We demonstrate their integrability by means of new Dunkl operators, associated to wreath products of dihedral groups.

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“…Further investigations, along the above lines are currently under progress and will be reported elsewhere. Recently, Calogero-Sutherland type models are also being extended to non-commutative spaces, 94 which has relevance to lowest Landau level physics. 95,96 Hence, extending the present approach to the noncommutative space is also an interesting area to explore.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Unified algebraic approach to few- and many-body correlated systems

Gurappa

Panigrahi

2003

Phys. Rev. B

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The present article is an extended version of the paper Phys. Rev. B 59, R2490 (1999, where, we have established the equivalence of the CalogeroSutherland model to decoupled oscillators. Here, we first employ the same approach for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few and many-body interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate new solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a novel method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system's wave functions, with those of the free particles on a circle. In the process, we obtain a new expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the ground-state and point out the natural emergence of the underlying linear W 1+∞ symmetry in this approach.

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Calogero-Moser Models with Noncommutative Spin Interactions

Cited by 20 publications

References 44 publications

Supersymmetric Calogero models by gauging

Supersymmetric Calogero models by gauging

Sutherland models for complex reflection groups

Unified algebraic approach to few- and many-body correlated systems

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