Quantum chaos in baryon spectra: Goldstone-boson versus one-gluon exchange

The Bohigas-Giannoni-Schmit conjecture for quantum chaos is formulated and evaluated within random-matrix theory. We discuss random-matrix theory as a tool to study the spectral behavior of an analytically solvable Hamiltonian, of a model Hamiltonian, and of experimental data. As a particular case we consider the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Preliminary results for the nucleon show that both types of interactions lead to a Wigner distribution, whereas a pure linear confinement potential exhibits a Brody distribution. (author)