Exactly solvable models of scattering with SL(2, C) symmetry

Research output: Contribution to journalArticle

Abstract

Using the theory of induced representations two exactly solvable models of non-relativistic scattering with SL(2, C) symmetry are presented. The first describes the scattering of a charged particle moving on the Poincaré upper half space H under the influence of an SU(2) non-Abelian gauge potential with isospin s. The second deals with a one-dimensional coupled-channel scattering problem for a charged particle in a matrix-valued scalar potential containing Morse-like interaction terms. The coupled channel wavefunctions and the corresponding scattering matrices are calculated. A detailed description of the underlying geometric structures is also given and a generalization for restricting the motion to fundamental domains of H (three manifolds of constant negative sectional curvature) is outlined. Such models provide an interesting generalization to the known ones of multichannel scattering, quantum chaos and chaotic cosmology.

Original languageEnglish
Pages (from-to)6431-6457
Number of pages27
JournalJournal of Physics A: Mathematical and General
Volume35
Issue number30
DOIs
Publication statusPublished - Aug 2 2002

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Exactly Solvable Models
Scattering
Symmetry
symmetry
scattering
Morse Potential
Fundamental Domain
Quantum Chaos
Induced Representations
Three-manifolds
Charged particles
charged particles
Scattering Matrix
Negative Curvature
Sectional Curvature
Geometric Structure
Scattering Problems
Cosmology
Half-space
Morse potential

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Exactly solvable models of scattering with SL(2, C) symmetry. / Lévay, P.

In: Journal of Physics A: Mathematical and General, Vol. 35, No. 30, 02.08.2002, p. 6431-6457.

Research output: Contribution to journalArticle

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