Derivation of Regge Trajectories from the Conservation of Angular Momentum in Hyperbolic Space

ABSTRACT

Regge trajectories can be simply derived from the conservation of angular momentum in hyperbolic space. The condition to be fulfilled is that the hyperbolic measure of distance and the azimuthal angle of rotation in the plane be given by the Bolyai-Lobachevsky angle of parallelism. Resonances or bound states that lie along a Regge trajectory are relativistic rotational states of the particle that are quantized by the condition that the difference in angular momentum between the rest mass, assumed to be the lead particle on the trajectory, and the relativistic rotational state is an integer. Since the hyperbolic expression for angular momentum is entirely classical, it cannot take into account signature, and whether exchange degeneracy is broken or not. However, the changes in the angular momentum are in excellent agreement with non-exchange degeneracy which assumes four different rest masses in the case of ρ, ω, a2, and f mesons trajectories, as well as in the case where there is only one rest mass in exchange degeneracy. A comparison is made between the critical and supercritical Pomeron trajectories; whereas the former has resonaces with higher masses, it has corresponding smaller linear dimensions.

Keywords:

Regge trajectories, conservation of angular momentum in hyperbolic space, relativistic rotational states.