Some baryons families exhibit a relation between the spin and mass, where the spin scales as the mass squared . In what follow we present a mechanical system that exhibits a similar relation between its mass and angular momentum. Let us consider rigid rod rotating in such a way that its ends are moving at the speed of light . Suppose that this rod has mass density per unit length and length , so its mass is . The angular velocity is given by . The energy of the string, even when its spinning, is proportional to the mass . The angular momentum is given by
Similar ideas are used in string theory to represent particles as modes in a vibrating string.
Simply speaking, there is a direct proportionality between the angular momentum and mass squared of some baryons e.g. the pi meson. This trajectory is the Regge trajectory. The angular momentum can take on any complex value and the Regge theory is nonrelativistic.
Regge trajectories are used to obtain potentials, for example, the quantum mechanical Coulomb potential and the Yukawa potential.