Quantum-relativistic rotator and oscillator models and their applications in hadron physics

The dissertation first contains some review sections on a Quantum Relativistic Rotator (QRR) and their predictions for the masses of the known hadrons. This work was developed by a large collaboration in Texas and other places. A joint feature of both these models is the Zitterbewegung whose classical form for the electron theory is revived in section I. For the models of the hadrons, the γ-matrices become hermitian operators of an infinite dimensional representation of SO(3,2). The second part of his dissertation describes his results for a new type of Quantum Relativistic Oscillator (QROII) which is also based on the spectrum generating group SO(3,2) but which differs from the standard Feynman's relativistic oscillator by its quantization. Their choice of quantization is analogous to the quantization of the internal variables of the Zitterbewegung. The resulting relativistic creation and annihilation operators only generate space-like oscillations and the oscillator has therefore a positive mass squared spectrum. The QROII contains a term that describes the Thomas precession and that generates a relativistic Coriolis force and a relativistic centrifugal force. The authors shows that all the nonrelativistic features are recovered when c goes to infinity. The QROII is then coupled to the electromagnetic field and they can calculate the radiative decay amplitudes of nucleon resonances from the interaction Hamiltonian