Quantized relativistic rotator
Abstract
The equations that describe the relativistic rotator classically are summarized to form a basis for the quantization. Strict adherence to the correspondence principle requires a Hamiltonian without any free parameters from which a linear wave equation is derived. The equations of motion of the various operators (in particular, those describing the Zitterbewegung) then depend only on the mass $M$ and the spin $s$. The angular frequency $\ensuremath{\omega}$ of the Zitterbewegung is found to be related to $M$ by $M{c}^{2}=(s+\frac{1}{2})\ensuremath{\hbar}\ensuremath{\omega}$. The simplest constraint relation needed to preserve these equations of motion while defining a spectrum requires that ${M}^{2}$ should be a linear function of $s$, in excellent agreement with the data on a number of hadron towers.