Quadratic Poisson algebras for two dimensional classical superintegrable systems and quadratic associative algebras for quantum superintegrable systems
Daskaloyannis, C.
arXiv, 0003017 / Harvested from arXiv
Text on arXiv
The integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable problem has a quantum counterpart, a quantum superintegrable system. The quadratic Poisson algebra is deformed to a quantum associative algebra, the finite dimensional representations of this algebra are calculated by using a deformed parafermion oscillator technique. It is shown that, the finite dimensional representations of the quadratic algebra are determined by the energy eigenvalues of the superintegrable system. The calculation of energy eigenvalues is reduced to the solution of algebraic equations, which are universal for all two dimensional superintegrable systems with quadratic integrals of motion.
Publié le : 2000-03-19
Classification:  Mathematical Physics,  Mathematics - Quantum Algebra,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Quantum Physics,  81R05,  81S05 
@article{0003017,
     author = {Daskaloyannis, C.},
     title = {Quadratic Poisson algebras for two dimensional classical superintegrable
  systems and quadratic associative algebras for quantum superintegrable
  systems},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0003017}
}

Daskaloyannis, C. Quadratic Poisson algebras for two dimensional classical superintegrable
  systems and quadratic associative algebras for quantum superintegrable
  systems. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0003017/