New angular momentum tensor for nucleon spin structure

New angular momentum tensor for nucleon spin structure Speaker: Zhen-Lai Wang, HUST Supervisor：Xiang-Song Chen 25 th July @ Hadron 2017

Contents: Ø Angular momentum decomposition: gauge invariance Ø New E-M tensor and A-M tensor Ø A new criterion: Constrains from quantum measurement ØApplications and Experimental tests

Angular momentum decomposition: 3

4

Which momentum: also important! Gluons carry not much momentum! 5

Scalar field can also have spin current! Wang, Z. -L. , Yang, D. -T. , Chen, Z. -W. , Lei, T. & Chen, X. -S. ar. Xiv: 1701. 08658 [hep-ph, physics: physics](2017) 6

Which one ? Why proposing another expression? Certainly because we found no existing ones fully satisfactory! 7

Conserved currents and its arbitrariness 8

A special criteria: Constrains 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. 9

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Mutual conservation of energy and momentum 11

Hyper-canonical currents: free field 12

How the hyper-canonical currents work 13

Alternative expression and additional spin current Scalar field can also have spin current! 14

Examples: photon 15

Hyper-canonical currents: derivation Noether currents by the revised Lagrangian 16

The interacting fields The total energy-momentum tensor: The total angular momentum tensor: 17

Application! Ø New light on neclueon spin structure Ø New gravitational coupling 18

! e g r a h c n i No extra sp 19

The gauge-invariant version ! e g r a h c n i No extra sp 20

Application: Consistent separation of nucleon momentum and spin van Enk, Nienhuis, J. Mod. Opt. 41: 963 (1994) Chen, Sun, Lü, Wang, Goldman, PRL 103: 062001 (2008) 21

The total action: The energy-momentum tensor: The spin tensor: The equations of gravitational field: Lei, T. , Chen, Z. -W. , Wang, Z. -L. & Chen, X. -S. ar. Xiv: 1702. 02921 [gr-qc](2017). 22

The scalar field: Einstein-Cartan theory 23

The vector field: Einstein-Cartan theory 24

Experimental test! Ø The ultimate test: Gravitation-coupling Ø Or: Should Einstein-Cartan theory be derived from a special flat-space Lagrangian (with second derivative) Ø Geometric spin hall effect Ø Or: Does photon/gluon has spin? 25

Geometric spin hall effect S L Theory: Aiello, A. , Lindlein, N. , Marquardt, C. & Leuchs, G. Phys. Rev. Lett. 103, 100401 (2009). Experiment: Korger, J. et al. Phys. Rev. Lett. 112, 113902 (2014) 25

Geometric spin hall effect of the light Prediction of the symmetric T ab: k--energy flux Prediction of the canonical and new T ab: T--momentum flux Wang, Z. -L. & Chen, X. -S. “Anomalous Geometric spin hall effect of the light? ” in preparation 27

Geometric spin hall effect of the electron Prediction of the symmetric T ab: k--energy flux T--momentum flux Prediction of the canonical and new T ab: 28

GSHE manifested as Moment of Force 29

Conclusions & Outlook • Reference: 1. Wang, Z. -L. , Yang, D. -T. , Chen, Z. -W. , Lei, T. & Chen, X. -S. ar. Xiv: 1701. 08658 [hep-ph, physics: physics](2017) 2. Lei, T. , Chen, Z. -W. , Wang, Z. -L. & Chen, X. -S. ar. Xiv: 1702. 02921 [gr-qc](2017). 3. Wang, Z. -L. & Chen, X. -S. “Anomalous Geometric spin hall effect of the light? ” in preparation 30

Thank you！ 谢谢！