Towards a final criteria of separating momentum and angular momentum Outline: I.The matter of convenience II.The matter of reasonableness III.The matter of correctness Xiang-Song Chen Huazhong University of Science & Technology 陈相松 华中科技大学 武汉 16 Feb INT-Seattle

Recall of the Controversies Leader [PRD 83: (2011)]

 Hint from a forgotten practice: Why photon is ignored for atomic spin?  The fortune of choosing Coulomb gauge  Quantitative differences  Fine-tuning for the gluon spin and OAM I. The matter of convenience and fine-tuning in actual application

Hint from a forgotten practice: Why photon is ignored for atomic spin? Do these solutions make sense?!

The atom as a whole

Close look at the photon contribution The static terms!

Justification of neglecting photon field

A critical gap to be closed

The same story with Hamiltonian

The fortune of using Coulomb gauge

Momentum of a moving atom A stationary electromagnetic field carries no momentum

Gauge-invariant revision – Angular Momentum

Gauge-invariant revision -Momentum and Hamiltonian

The covariant scheme spurious photon angular momentum

Gluon angular momentum in the nucleon: Tree-level One-gluon exchange has the same property as one-photon exchange

Beyond the static approximation

Fine-tuning for the gluon spin and OAM Possible convergence in evolution

 Leader’s compelling criteria to remove the controversy  Recalling the Poincare algebra and subalgebra for and interacting system  Generators for the physical fields: QED  The quark-gluon system II. The matter of reasonableness ---Leader’s criteria of separating momentum and angular momentum

The controversy and Leader’s Criteria

Interacting theory: Structure of Poincare generators

Interacting theory: Poincare (sub)algebra

Generators for the gauge-invariant physical fields - translation

Generators for the gauge-invariant physical fields - Rotation

The quark-gluon system

Generator for the gauge- invariant quark field

Generator for the gauge- invariant gluon field

Some detail in the proof

III. Possibly a real final solution Dipole rad. (rad. gauge) l=1 m=1 E Flux J Flux

Miracle of quantum Measurement A system can only be detected in certain eigenstate E.g. Optical pumping of a trapped ion

The issue of “indirect” observable in QCD: matter of definition, but …  The same experiments as to “measure” the conventional PDFs  New factorization formulae and extraction of the new PDFs  Quark and gluon orbital angular momentum can in principle be measured through generalized (off- forward) PDFs

Is gauge-invariance a “Compromise”, or even “illusion”?  First step in Physics ： Complete Description  Classic Physics: r and p （ controllable ）  Quantum Mechanics ： Wave Function （ Not completely controllable ）  Gauge Theory ： Gauge potentials (Completely uncontrollable ） Need for the physical variable: Real emergence of a photon

Thank you! 谢谢 !