Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine ${\mathfrak{sl}}_2$ Gaudin model

Abstract

In this work we will use a general procedure to construct higher local Hamiltonians for the affine ${\mathfrak{sl}}_2$ Gaudin model. We focus on the first non-trivial example, the quartic Hamiltonians. We show by direct calculation that the quartic Hamiltonians commute amongst themselves and with the quadratic Hamiltonians which define the model. We go on to introduce a certain next-to-leading-order semi-classical limit of the model. In this limit, we are able to write down the full hierarchy of higher local Hamiltonians and prove that they commute.

32 pages,1 figure. Accepted version for J. Phys. A: Math. Theor

References in corpus (5)

• Quantization of the Gaudin System
• Bethe eigenvectors of higher transfer matrices
• Schubert calculus and representations of general linear group
• Quantization of soliton systems and Langlands duality
• Critical points of master functions and flag varieties

Cited by in corpus (5)

• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• An elliptic integrable deformation of the Principal Chiral Model
• On a class of conformal $\mathcal{E}$-models and their chiral Poisson algebras
• Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex
• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model