Geodesic
Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb--Dirac Field
Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 3, pp. 424-454

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The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues.
Keywords: integrable systems, nonlinear commutation relations, coherent states, asymptotic spectrum behavior.
Mots-clés : Dirac monopole 
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     author = {M. V. Karasev and E. M. Novikova},
     title = {Algebra with {Quadratic} {Commutation} {Relations} for an {Axially} {Perturbed} {Coulomb--Dirac} {Field}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2004_141_3_a6/}
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M. V. Karasev; E. M. Novikova. Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb--Dirac Field. Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 3, pp. 424-454. http://geodesic.mathdoc.fr/item/TMF_2004_141_3_a6/