Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine s l 2 Gaudin model

Tommaso Franzini, Charles Young

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Abstract

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 Hamiltonians and prove that they commute.
Original languageEnglish
Article number105201
Pages (from-to)1-25
Number of pages25
JournalJournal of Physics A: Mathematical and Theoretical
Volume56
Issue number10
DOIs
Publication statusPublished - 21 Feb 2023

Keywords

  • Paper
  • Mathematical physics
  • integrable models
  • integrable systems
  • affine Gaudin models
  • Gaudin models
  • higher Hamiltonians
  • sl2 Gaudin model
  • higher Hamiltonians at leading order

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