The QCD string and the generalised wave equation

TL;DR

This paper reviews a generalized wave equation for the QCD string, introducing infinite-dimensional gamma matrices that ensure unitarity and reveal a spectrum of charged particles with specific degeneracies, differing from superstring theory.

Contribution

It proposes a generalized Dirac form of the QCD string equation with novel gamma matrices, ensuring unitarity and a distinct particle spectrum.

Findings

Gamma matrices are symmetric solutions of Majorana relations.

The spectrum includes charged particles with spins from 1/2 to r-1/2.

Degeneracy of states is linear, not exponential as in superstring theory.

Abstract

The equation for QCD string proposed earlier is reviewed. This equation appears when we examine the gonihedric string model and the corresponding transfer matrix. Arguing that string equation should have a generalized Dirac form we found the corresponding infinite-dimensional gamma matrices as a symmetric solution of the Majorana commutation relations. The generalized gamma matrices are anticommuting and guarantee unitarity of the theory at all orders of $v/c$. In the second quantized form the equation does not have unwanted ghost states in Fock space. In the absence of Casimir mass terms the spectrum reminds hydrogen exitations. On every mass level $r=2,4,..$ there are different charged particles with spin running from $j=1/2$ up to $j_{max}=r-1/2$, and the degeneracy is equal to $d_{r}=2r-1 = 2j_{max}$. This is in contrast with the exponential degeneracy in superstring theory.