1. 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 2012 @ INT-Seattle

2. Recall of the Controversies Leader [PRD 83:096012 (2011)]

3.  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

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

5. The atom as a whole

6. Close look at the photon contribution The static terms!

7. Justification of neglecting photon field

8. A critical gap to be closed

9. The same story with Hamiltonian

10. The fortune of using Coulomb gauge

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

12. Gauge-invariant revision – Angular Momentum

13. Gauge-invariant revision -Momentum and Hamiltonian

14. The covariant scheme spurious photon angular momentum

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

16. Beyond the static approximation

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

18.  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

19. The controversy and Leader’s Criteria

20. Interacting theory: Structure of Poincare generators

21. Interacting theory: Poincare (sub)algebra

22. Generators for the gauge-invariant physical fields - translation

23. Generators for the gauge-invariant physical fields - Rotation

24. The quark-gluon system

25. Generator for the gauge- invariant quark field

26. Generator for the gauge- invariant gluon field

27. Some detail in the proof

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

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

30. 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

31. 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

32. Thank you! 谢谢 !