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Towards a final criteria of separating momentum and angular momentum

This article discusses the criteria for separating momentum and angular momentum in physics. It explores the matter of convenience, reasonableness, and correctness in making these distinctions. The author, Xiang-Song Chen from Huazhong University of Science & Technology, presents a comprehensive analysis of the topic. The article is written in English.

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Towards a final criteria of separating momentum and angular momentum

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  1. Towards a final criteria of separating momentum and angular momentum Outline: The matter of convenience The matter of reasonableness 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. I. The matter of convenience and fine-tuning in actual application • 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

  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. II. The matter of reasonableness ---Leader’s criteria of separating momentum and angular momentum • 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

  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!

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