[Paper Review] Gauge invariance and hadron structure

Xiang-Song Chen, Fan Wang|ArXiv.org|Feb 18, 1998

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proves that gauge-dependent operators for gluon spin, quark and gluon orbital angular momentum, and momentum components yield gauge-invariant expectation values on hadron states with definite momentum and polarization. The key result is that the conventional decomposition of nucleon spin and momentum into quark and gluon contributions is gauge invariant, resolving long-standing concerns about gauge dependence in hadron structure physics.

ABSTRACT

We prove that the {\em gauge dependent} gluon spin, gluon and quark orbital angular momenta operators have {\em gauge invariant} expectation values on hadron states with {\em definite} momentum and polarization, therefore the conventional decomposition of nucleon spin into contributions from the spin and orbital angular momentum of quark and gluon is {\em gauge independent}. Similar conclusions apply to the {\em gauge dependent} quark momentum and kinetic energy operators, and accordingly nucleon momentum and mass structures.

Motivation & Objective

• To resolve the long-standing debate on whether the decomposition of nucleon spin and momentum into quark and gluon contributions is gauge dependent.
• To establish that gauge-dependent operators for spin and orbital angular momentum yield gauge-invariant expectation values on physical hadron states.
• To clarify the theoretical foundation of the parton model and generalized parton distributions in quantum chromodynamics (QCD).
• To address apparent contradictions with earlier calculations by Hoodbhoy, Ji, and Lu regarding gauge dependence in nucleon structure.
• To provide a rigorous, comprehensive proof of gauge invariance in hadron structure observables using field-theoretic methods.

Proposed method

• Uses canonical quantization and gauge field theory to define gauge-dependent operators for gluon spin, orbital angular momentum, and momentum.
• Applies the requirement of definite momentum and polarization to physical hadron states to constrain operator expectation values.
• Demonstrates that despite gauge dependence of individual operators, their expectation values on physical states are gauge invariant.
• Employs a systematic field-theoretic approach to show that physical observables are independent of gauge choice.
• Reconciles apparent contradictions with prior work by analyzing the role of boundary conditions and physical state projection.
• Uses the framework of relativistic quantum field theory to prove that gauge invariance is preserved in matrix elements on on-shell hadron states.

Experimental results

Research questions

• RQ1 Are the decomposition of nucleon spin into quark and gluon contributions gauge invariant?
• RQ2 Can gauge-dependent operators yield gauge-invariant expectation values on physical hadron states?
• RQ3 How does the gauge invariance of matrix elements reconcile with earlier claims of gauge dependence in nucleon structure?
• RQ4 What is the role of momentum and polarization eigenstates in ensuring gauge invariance of spin and momentum decomposition?
• RQ5 Why do certain calculations, such as those by Hoodbhoy, Ji, and Lu, not contradict the theorem of gauge invariance presented here?

Key findings

• The expectation values of gauge-dependent operators for gluon spin, quark and gluon orbital angular momentum, and momentum are gauge invariant on hadron states with definite momentum and polarization.
• The conventional decomposition of nucleon spin into quark and gluon contributions is therefore gauge independent, resolving a central issue in hadron structure physics.
• The proof is complete and comprehensive, explicitly showing that gauge invariance is preserved in matrix elements on physical states.
• The authors demonstrate that the calculations of Hoodbhoy, Ji, and Lu do not contradict their theorem, as they do not consider the full physical state projection.
• The result extends to nucleon momentum and mass structure, confirming that these decompositions are also gauge invariant.
• The work establishes a rigorous foundation for interpreting experimental data on nucleon spin and momentum distributions in terms of quark and gluon contributions.