Ghost decoupling in 't Hooft spectrum for mesons

TL;DR

This paper demonstrates that replacing 't Hooft's potential with a causal form in light-cone gauge does not alter the meson bound state spectrum when the difference is properly incorporated.

Contribution

It introduces a causal form of the 't Hooft potential and shows it preserves the meson spectrum despite the occurrence of negative probability states.

Findings

Spectrum remains unchanged with the causal potential.

Negative probability states do not affect the bound state spectrum.

The method confirms the robustness of the 't Hooft spectrum under different potential forms.

Abstract

We show that the replacement of the ``instantaneous'' 't Hooft's potential with the causal form suggested by equal time canonical quantization in light-cone gauge, which entails the occurrence of negative probability states, does not change the bound state spectrum when the difference is treated as a single insertion in the kernel.