1/N corrections in Calogero-type models using the collective-field method

Andrić, Ivan; Bardek, V.

doi:10.1088/0305-4470/21/13/009

Cited by 25 publications

(27 citation statements)

References 8 publications

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“…In this Letter we investigate solitons in the CSM in terms of the collective-field Hamiltonian description formulated in ref. [4,7]. We briefly mention the results of ref.…”

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confidence: 87%

“…The CSM also appears when two-dimensional QCD is formulated as a random matrix model in the large-N limit, restricted to a singlet subspace [4]. For a one-dimensional free fermionic Fock space, which is described by a hermitian matrix model [5], the collectivefield Hamiltonian can be introduced [6].…”

mentioning

confidence: 99%

“…This can be seen when the collective-field formulation is written for CSM, as was done in ref. [4,7]. The hole excitations in the spectrum are represented as a soliton of the Calogero-Sutherland collective-field theory.…”

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confidence: 99%

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Solitons in the Calogero-Sutherland collective-field model

1995

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“…In this Letter we investigate solitons in the CSM in terms of the collective-field Hamiltonian description formulated in ref. [4,7]. We briefly mention the results of ref.…”

mentioning

confidence: 87%

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confidence: 99%

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Solitons in the Calogero-Sutherland collective-field model

1995

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“…We may therefore set θ(x) = −iδ/δρ(x), and try to find eigenstates of the Hamiltonian (9) as functionals of ρ(x). Although this is sometimes possible [23], it is generally very difficult to find exact eigenstates.…”

Section: Calogero-sutherland Model and Collective Field Theorymentioning

confidence: 99%

Applications of the Collective Field Theory for the Calogero–Sutherland Model

Sen

Bhaduri

1997

Annals of Physics

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We use the collective field theory known for the Calogero-Sutherland model to study a variety of low-energy properties. These include the ground state energy in a confining potential upto the two leading orders in the particle number, the dispersion relation of sound modes with a comparison to the two leading terms in the low temperature specific heat, large amplitude waves, and single soliton solutions. The two-point correlation function derived from the dispersion relation of the sound mode only gives its nonoscillatory asymptotic behavior correctly, demonstrating that the theory is applicable only for the low-energy and long wavelength excitations of the system.

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“…(1.1) where H sing denotes a singular contribution [4,5] 2) and P is the principal part symbol. Here,…”

Section: Introductionmentioning

confidence: 99%

Fluctuations around periodic BPS-density waves in the Calogero model

Bardek

Feinberg

Meljanac

2010

J. High Energ. Phys.

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Abstract:The collective field formulation of the Calogero model supports periodic density waves. An important set of such density waves is a two-parameter family of BPS solutions of the equations of motion of the collective field theory. One of these parameters is essentially the average particle density, which determines the period, while the other parameter determines the amplitude. These BPS solutions are sometimes referred to as "small amplitude waves" since they undulate around their mean density, but never vanish. We present complete analysis of quadratic fluctuations around these BPS solutions. The corresponding fluctuation hamiltonian (i.e., the stability operator) is diagonalized in terms of bosonic creation and annihilation operators which correspond to the complete orthogonal set of Bloch-Floquet eigenstates of a related periodic Schrödinger hamiltonian, which we derive explicitly. Remarkably, the fluctuation spectrum is independent of the parameter which determines the density wave's amplitude. As a consequence, the sum over zero-point energies of the field-theoretic fluctuation hamiltonian, and its ensuing normal-ordering and regularization, are the same as in the case of fluctuations around constant density background, namely, the ground state. Thus, quadratic fluctuations do not shift the energy density tied with the BPS-density waves studied here, compared to its ground state value. Finally, we also make some brief remarks concerning fluctuations around non-BPS density waves.

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1/N corrections in Calogero-type models using the collective-field method

Cited by 25 publications

References 8 publications

Solitons in the Calogero-Sutherland collective-field model

Solitons in the Calogero-Sutherland collective-field model

Applications of the Collective Field Theory for the Calogero–Sutherland Model

Fluctuations around periodic BPS-density waves in the Calogero model

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