Quartic Hamiltonians, and higher Hamiltonians at nexttoleading 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 nontrivial 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 nexttoleadingorder semiclassical 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2023
 DOI:
 10.1088/17518121/acbacf
 arXiv:
 arXiv:2205.15815
 Bibcode:
 2023JPhA...56j5201F
 Keywords:

 integrable models;
 integrable systems;
 affine Gaudin models;
 Gaudin models;
 higher Hamiltonians;
 sl2 Gaudin model;
 higher Hamiltonians at leading order;
 Mathematics  Quantum Algebra;
 High Energy Physics  Theory
 EPrint:
 32 pages,1 figure. Accepted version for J. Phys. A: Math. Theor