Relativistic rotator. I. Quantum observables and constrained Hamiltonian mechanics

Abstract

The model of the quantum relativistic rotator is defined by three correspondences: (1) the correspondence to a classical relativistic rotator when the quantum description goes over into the classical description (classical limit), (2) the correspondence to an elementary particle when the structure is ignored (elementary limit), and (3) the correspondence to a nonrelativistic quantum rotator (a rigid rotating string) in the nonrelativistic limit. The dynamics is given by a Hamiltonian which is obtained from a constraint relation that leads to a phenomenologically acceptable mass-spin trajectory relation. From the equation of motion it follows that the expectation value of the particle position spirals with approximately the velocity of light about the direction of the momentum, which is also the direction in which the center of mass propagates. The radius of this helical motion (i.e., the "size" of the rotator), as obtained from the phenomenological mass spectrum, is of the order of 10^-13 cm.