Errors in the Bag Model of Strings, and Regge Trajectories Represent the Conservation of Angular Momentum in Hyperbolic Space

TL;DR

This paper critiques the MIT bag model, shows errors in deriving Regge trajectories, and explains these trajectories as conservation of angular momentum in hyperbolic space, aligning well with experimental data.

Contribution

It corrects the derivation of Regge trajectories using hyperbolic geometry and clarifies their physical interpretation as angular momentum conservation.

Findings

MIT bag model assumptions are invalid.

Regge trajectories derived from hyperbolic geometry match experimental data.

Angular momentum conservation in hyperbolic space explains Regge trajectories.

Abstract

The MIT bag model is shown to be wrong because the bag pressure cannot be held constant, and the volume can be fixed in terms of it. The bag derivation of Regge's trajectories is invalidated by an integration of the energy and angular momentum over all values of the radius up to $r_0=c/\omega$. This gives the absurd result that "total" angular momentum decreases as the frequency increases. The correct expression for the angular momentum is obtained from hyperbolic geometry of constant negative curvature $r_0$. When the square of the relativistic mass is introduced, it gives a negative intercept which is the Euclidean value of the angular momentum. Regge trajectories are simply statements of the conservation of angular momentum in hyperbolic space. The frequencies and values of the angular momentum are in remarkable agreement with experiment.