Solvability of the Hamiltonians related to exceptional root spaces: Rational case
Por:
Boreskov K.G., Turbiner A.V., Vieyra J.C.L.
Publicada:
1 ene 2005
Resumen:
Solvability of the rational quantum integrable systems related to exceptional root spaces G 2,F 4 is re-examined and for E 6,7,8 is established in the framework of a unified approach. It is shown that Hamiltonians take algebraic form being written in certain Weyl-invariant variables. It is demonstrated that for each Hamiltonian the finite-dimensional invariant subspaces are made from polynomials and they form an infinite flag. A notion of minimal flag is introduced and minimal flag for each Hamiltonian is found. Corresponding eigenvalues are calculated explicitly while the eigenfunctions can be computed by pure linear algebra means for arbitrary values of the coupling constants. The Hamiltonian of each model can be expressed in the algebraic form as a second degree polynomial in the generators of some infinite-dimensional but finitely-generated Lie algebra of differential operators, taken in a finite-dimensional representation. © Springer-Verlag 2005.
Filiaciones:
Boreskov K.G.:
Institute for Theoretical and Experimental Physics, Moscow 117259, Russian Federation
Turbiner A.V.:
Instituto de Ciencias Nucleares, UNAM, A.P. 70-543, 04510 Mexico D.F., Mexico
Vieyra J.C.L.:
Instituto de Ciencias Nucleares, UNAM, A.P. 70-543, 04510 Mexico D.F., Mexico
|