Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems

Details Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems

2002-12-10

arxiv.org/abs/hep-th/0212117v4

J.Phys.A36:11299-11319,2003

Physics

High Energy Physics

High Energy Physics - Theory

25 pages; ref added; to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/36/44/009

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

Affiliated with

Also associated with

No associations

Rating

Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-638049