1. Art of Spin Decomposition --- A practical perspective
Xiang-Song Chen
Huazhong University of Science & Technology
陈相松 •华中科技大学•武汉
Oct 5th @ Spin 2015

2. Recall of the Controversies: gauge invariance

3. A practical perspective:
Construction of Spin Eigenstate
Simplification of Spin Structure
Experimental differentiation of Spin from OAM
Enlarged inspection: The angular momentum tensor and flux density

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. Gauge-invariant revision
– Angular Momentum

12. Gauge-invariant revision -Momentum and Hamiltonian

13. spurious photon angular momentum
The covariant scheme 
spurious photon angular momentum

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

15. Physical part of the non-Abelian gluon field

16. Manipulating the gluon spin

17. Beyond the static approximation

18. A key issue in spin decomposition
Should we separate spin from OAM?

19. The Experimental answer: two kinds of angular momenta
Spin is a kind of angular momentum without circulation of momentum

20. the angular momentum tensor Surprising: none is satisfactory!
Enlarged inspection:
the angular momentum tensor
Surprising: none is satisfactory!

21. A new perspective: Constrains on Tab from quantum measurement
If a quantum wave is in mutual eigenstates of more than one observables, then the associated currents must be proportional to each other

22. The Symmetric Tab stands no chance!
But the canonical Tab is not fully OK

23. An improved Tab: free field
E.g. photon

24. Proof of validness (general free fields)

25. The interacting fields: scalar case
This gives a gravitational theory different from Einstein’s GR

26. Trouble with the Angular momentum tensor
Our trick applies to longitudinal spin flux only, but not to transverse flux of angular momentum!

27. And thus no satisfactory way of spin decomposition.
Conclusion:
So far there exists no satisfactory expression of angular momentum tensor, even for a free field!
And thus no satisfactory way of spin decomposition.
Thank you! 27