The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
Integrable Hierarchy of the Quantum Benjamin-Ono Equation
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abstract
A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables $x_1,x_2,\ldots$. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions $p_n=x_1^n+x_2^n+\cdots$ and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849, arXiv:1212.2781].
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A superintegrable quantum field theory
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.