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

@inproceedings{Franzini2022QuarticHA, title={Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine \$\mathfrak\{sl\}\_2\$ Gaudin model}, author={Tommaso Franzini and Charles A. S. Young}, year={2022} }

In this work we will use a general procedure to construct higher local Hamiltonians for the affine sl2 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…

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