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Poincare sub-algebra and gauge invariance in nucleon structure

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

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

  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. A practical thinking about nucleon structure • 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

  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

  31. S. Weinberg, Phys. Rev. 138 (1965) B988

  32. 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)XU(1) and Higgs?

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

  42. Summary 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. If adopting the naive free-form expression, Coulomb gauge gives the simplest pictures for atomic and nucleon structure. 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.

  43. Thank you! 谢谢!