F-4 Quantum Integrable, rational and trigonometric models: space-of-orbits view
Por:
Turbiner A.V., Vieyra J.C.L.
Publicada:
1 ene 2014
Categoría:
Physics and Astronomy (miscellaneous)
Resumen:
Algebraic-rational nature of the four-dimensional, F-4-invariant
integrable quantum Hamiltonians, both rational and trigonometric, is
revealed and reviewed. It was shown that being written in F-4 Weyl
invariants, polynomial and exponential, respectively, both
similarity-transformed Hamiltonians are in algebraic form, they are
quite similar the second order differential operators with polynomial
coefficients; the flat metric in the Laplace-Beltrami operator has
polynomial (in invariants) matrix elements. Their potentials are
calculated for the first time: they are meromorphic (rational) functions
with singularities at the boundaries of the configuration space. Ground
state eigenfunctions are algebraic functions in a form of polynomials in
some degrees. Both Hamiltonians preserve the same infinite, flag of
polynomial spaces with characteristic vector (1, 2, 2, 3), it manifests
exact solvability. A particular integral common for both models is
derived. The first polynomial eigenfunctions are presented explicitly.
Filiaciones:
Turbiner A.V.:
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 México D.F, Mexico
Vieyra J.C.L.:
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 México D.F, Mexico
|