General intrinsic theory of general large $N_{c}$ QCD, SU(3) QCD, SU(2) hadron-dynamics and U(1) QED gauge field theories in general field theory and progress towards solving the nucleon spin crisis

TL;DR

This paper develops a comprehensive intrinsic theory for large $N_{c}$ QCD and related gauge theories, revealing their internal structures, gauge-invariant angular momenta, and new Coulomb theorems, advancing understanding of the nucleon spin crisis.

Contribution

It introduces a novel gauge potential decomposition technique and derives gauge-invariant spin and orbital angular momentum operators, addressing key issues in nucleon spin structure and strong interaction theories.

Findings

Discovered covariant transverse and parallel conditions in large $N_{c}$ QCD

Established gauge-invariant angular momentum operators for quark and gauge fields

Proposed a new gauge potential decomposition method

Abstract

This paper gives general intrinsic theory of general large $N_{c}$ QCD, SU(3) QCD, SU(2) hadron-dynamics and U(1) QED gauge field theories in general field theory and progress towards solving the nucleon spin crisis, i.e., presents general large $N_{c}$ QCD's inner structures, gauge invariant angular momenta and new corresponding Coulomb theorem in quark-gluon field interaction systems based on general field theory, and naturally deduces the gauge invariant spin and orbital angular momentum operators of quark and gauge fields with $SU(N_{c})$ gauge symmetry by Noether theorem in general field theory. In the general large $N_{c}$ QCD, we discover not only the general covariant transverse and parallel conditions ( namely, non-Abelian divergence and curl ), but also that this general system has good intrinsic symmetry characteristics. Specially, this paper's generally decomposing gauge potential theory presents a new technique, it should play a votal role in future physics research. Therefore, this paper breakthroughs the some huge difficulties in the nucleon spin crisis and opens a door of researching on lots of strong interacting systems with different symmetric properties, which is popularly interesting, and keeps both the gauge invariance and their angular momentum commutation relations so that their theories are consistent. Especially, the achieved results here can be utilized to calculate the general QCD strong interactions and to give the precise predictions that can be exactly measured by current particle physics experiments due to their gauge invariant properties etc.