The Heun Equation and the Calogero-Moser-Sutherland System I: The Bethe Ansatz Method

Takemura, Kouichi

doi:10.1007/s00220-002-0784-2

Cited by 57 publications

(155 citation statements)

References 7 publications

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“…From the comparison between (2.25) and (2.26) we finally extract the leading semiclassical expression for the residue of this 3-particle process 27) and therefore the 3-particle coupling 4…”

Section: Classical Solutions In Finite Volumementioning

confidence: 99%

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Kink scaling functions in 2D non-integrable quantum field theories

et al. 2006

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We determine the semiclassical energy levels for the φ 4 field theory in the broken symmetry phase on a 2D cylindrical geometry with antiperiodic boundary conditions by quantizing the appropriate finite-volume kink solutions. The analytic form of the kink scaling functions for arbitrary size of the system allows us to describe the flow between the twisted sector of c = 1 CFT in the UV region and the massive particles in the IR limit. Kink-creating operators are shown to correspond in the UV limit to disorder fields of the c = 1 CFT. The problem of the finite-volume spectrum for generic 2D Landau-Ginzburg models is also discussed.

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Section: Classical Solutions In Finite Volumementioning

confidence: 99%

“…We will now present the solutions of the Lamé equation for N = 1 and N = 2, which have been derived in [27,28] together with more complicated cases.…”

Section: B Lamé Equationmentioning

confidence: 99%

Kink scaling functions in 2D non-integrable quantum field theories

et al. 2006

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“…It is worth noting that these strings are related to the above-mentioned possibility to multiply (3.10) by an entire function of x L . § Takemura [25] has also discussed the application of BAE to the determination of zeroes of wave functions for the generalised Pöschl-Teller equation (or the BC1 Calogero-Sutherland model), however, with the L2 property. The BAE itself is similar to the semi-classical form, thus different from that described here, the quantum form.…”

Section: The Bethe Ansatz Equations and String Like Solutionsmentioning

confidence: 99%

Finite lattice Bethe ansatz systems and the Heun equation

Dorey¹,

Suzuki²,

Tateo³

2004

J. Phys. A: Math. Gen.

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We study the Pöschl-Teller equation in complex domain and deduce infinite families of T Q and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms of the Heun function. At particular values there is a interesting interpretation in terms of finite lattice spin-XXZ quantum chain with ∆ = cos π L (for free-free boundary conditions), or ∆ = − cos π L (for periodic boundary conditions). This result generalises the findings of Fridkin, Stroganov and Zagier. We also discuss the continuous (field theory) limit of these systems in view of the so-called ODE/IM correspondence.PACS number: 05.50+q, 02.30.Ik

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“…Hence the monodromy of eigenfunctions of H 1 corresponding to the eigenvalue E coincides with that of the eigenfunctions of H 2 , although the expression of the functions Λ 1 (x, E) and Λ 2 (x, E) is quite different (see section 7). In this paper, we investigate these phenomena by means of the Darboux transformation and generalized Darboux transformation.…”

Section: )mentioning

confidence: 99%

“…Set where ℘(x) is the Weierstrass ℘-function with periods (2ω 1 , 2ω 3 ) and ω 2 = −ω 1 − ω 3 . For the operators H 1 and H 2 , we have integral representations of eigenfunctions for any eigenvalues, and the monodromy of eigenfunctions is calculated in terms of hyperelliptic integrals (see [7,9,10]). It is shown that there exist eigenfunctions Λ 1 (±x, E) (resp.…”

Section: Introductionmentioning

confidence: 99%

The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

Takemura¹

2006

JNMP

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We obtain isomonodromic transformations for Heun's equation by generalizing the Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures that the finite-gap property is satisfied. As an application, we prove some previous conjectures in part III.

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The Heun Equation and the Calogero-Moser-Sutherland System I: The Bethe Ansatz Method

Cited by 57 publications

References 7 publications

Kink scaling functions in 2D non-integrable quantum field theories

Kink scaling functions in 2D non-integrable quantum field theories

Finite lattice Bethe ansatz systems and the Heun equation

The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

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