1. Poincare sub-algebra and gauge invariance in nucleon structure Xiang-Song Chen Huazhong University of Science & Technology 陈相松 华中科技大学 武汉 10 July 2012 @ KITPC-Beijing

2. I.Controversy in nucleon (spin) structure II.Elliot Leader’s criteria of separating momentum and angular momentum III.Reconciling Poincare sub-algebra with gauge invariance IV.A practical thinking about nucleon structure V.A critical thinking about gauge invariance Outline

3. Nucleon spin comes from the polarization and orbital motion of quarks and gluons --- Chairman Mao A universally correct statement for the nucleon spin

4. Controversy in nucleon spin structure Leader [PRD 83:096012 (2011)]

5. Interacting theory: Structure of Poincare generators Without gauge symmetry, the issue is trivial:

6. Interacting theory: Poincare (sub)algebra

7. Further criteria by Elliot Leader Corollary

8. Examination of various decompositions by Leader’s criteria Leader [PRD 83:096012 (2011)]

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

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

11. The quark-gluon system

12. Generator for the gauge- invariant quark field

13. Generator for the gauge- invariant gluon field

14. Some detail in the proof

15.  Hint from a forgotten practice: Why photon is ignored for atomic spin?  The fortune of choosing Coulomb gauge  Quantitative differences  Another example: momentum of a moving atom and nucleon A practical thinking about nucleon structure

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

17. The atom as a whole

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

19. Justification of neglecting photon field

20. A critical gap to be closed

21. The same story with Hamiltonian

22. The fortune of using Coulomb gauge

23. Gauge-invariant revision – Angular Momentum

24. Gauge-invariant revision -Momentum and Hamiltonian

25. The covariant scheme spurious photon angular momentum

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

27. Beyond the static approximation

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

29. Quark and gluon momentum in the nucleon

30. Weinberg’s approach: derivation of QED with physical photons S. Weinberg, Phys. Rev. 138 (1965) B988

33. The non-covariant propagator of Physical photon

34. A delicate point: the contact term and its effect

35. Cancelation of the contact term

36. 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

37. A possible real difference Dipole rad. (rad. gauge) l=1 m=1 E Flux J Flux

38. If we never need physical gluons …… Then QCD is a true gauge theory, and the only try gauge theory so far known And all quark and gluon quantities are a matter of definition

39. Do we sometimes need physical gluons? Probably, in early universe Then color gauge invariance may also be an illusion!

40. What about SU(2) X U(1) and Higgs?

41. Derivation of non-Abelian gauge theory with physical gluons by requiring Lorentz invariance??? Derivation of QED with physical photons by requiring Lorentz invariance

42. I.Nucleon spin and momentum can be separated gauge invariantly, with quark/gluon part acting as the rotation and translation generators for the physical quark/gluon field. II.If adopting the naive free-form expression, Coulomb gauge gives the simplest pictures for atomic and nucleon structure. III.Gauge symmetry might be an illusion. QED can be derived from physical photons by requiring Lorentz invariance of S matrix, but the situation for non- Abelian theory is more tricky and not yet proven. demonstrated. Summary

43. Thank you! 谢谢 !