The Lineage of String Theory

TL;DR

This paper explores the historical and mathematical foundations of string theory, emphasizing the behavior of Regge trajectories, their relation to other fundamental interactions, and the geometric and automorphic functions involved.

Contribution

It provides a novel perspective on string theory's foundations by linking Regge trajectories to gravity and gauge interactions, and discusses automorphic functions and geometric transformations in this context.

Findings

Regge trajectories behave as rigid rotators, not vibrating strings.

Relations between angular momentum and mass squared are common across fundamental interactions.

Automorphic functions and geometric transformations underpin the mathematical structure of the theory.

Abstract

The Regge trajectories, upon which string theory is based, behave as rigid rotators rather than vibrating strings. The same relation, between the angular momentum, and the square of the mass, can be found in gravity, the electroweak, and strong interactions. The angle deficit for cosmic strings is shown to be an angle excess that is related to the increase of the circumference of a uniformly rotating disc. Schr\"odinger's time independent equation with a centrifugal barrier gives an automorphic function that can be constructed as the ratio of its two independent solutions for values of the angular momentum lying outside of their positive, integer values. If the fixed points 0 and $\infty$ in the z-plane correspond to $-i$ and $+i$ in the $\omega$-plane, then elliptic substitutions tessellate the $\omega$-plane in the form of cresents, while if the fixed points correspond to -1 and +1 in the $\omega$-plane are source and sink, just like the lines of force between positive and negative charges. The unit disc undergoes a stretching by a Lorentz transform.