art of spin decomposition
DESCRIPTION
Art of Spin Decomposition. Outline: Spin sum rules and controversies A most familiar example What makes a good spin decomposition Angular momentum of tensor gauge field Critical thinking about gauge invariance. Xiang-Song Chen 陈相松 Huazhong Univ. of Sci. & Tech. 华中科技大学. - PowerPoint PPT PresentationTRANSCRIPT
Art of Spin Decomposition
Xiang-Song Chen 陈相松Huazhong Univ. of Sci. & Tech. 华中科技大学
Outline:
Spin sum rules and controversies
A most familiar example
What makes a good spin decomposition
Angular momentum of tensor gauge field
Critical thinking about gauge invariance
Related recent papers1) Art of spin decomposition Xiang-Song Chen, Wei-Min Sun, Fan Wang, T. Goldman, Phys. Rev. D 83, 071901(R) (2011).
2) Proper identification of the gluon spin Xiang-Song Chen, Wei-Min Sun, Fan Wang, T. Goldman, Phys. Lett. B 700, 21 (2011).
3) Physical decomposition of the gauge and gravitational fields Xiang-Song Chen, Ben-Chao Zhu, Phys. Rev. D 83, 084006 (2011).
4) Spin and orbital angular momentum of the tensor gauge field. Xiang-Song Chen, Ben-Chao Zhu, Niall Ó Murchadha, arXiv:1105.6300v1
5) Tensor gauge condition and tensor field decomposition Xiang-Song Chen, Ben-Chao Zhu, arXiv:1101.2809v4
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Earlier and recent Spin sum rules
A most familiar example: Solving the hydrogen atom
Does this make sense???
The atom as a whole
Close look at the photon contribution
The static terms!
Justification of neglecting photon field
A critical gap to be closed
The same story with Hamiltonian
The fortune of using Coulomb gauge
Momentum of a moving atom
A stationary electromagnetic field carries no momentum
Gauge-invariant revision
The covariant scheme
spurious photon angular momentum
Gluon angular momentum in the nucleon:
Tree-level
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BErxdJ g
One-gluon exchange has the same property as
one-photon exchange
Beyond the static approximation
The tensor gauge field
Canonical expression of spin and OAM
Canonical expression of spin and OAM
Complete tensor gauge conditions
Vanishing of angular momentum for a stationary tensor gauge field
No spurious time-
dependence
The same property of momentum
Critical thinking about gauge invariance: Gauge theory as a “Compromising” Physical Theory
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)
Conditions Results
Gauge invariance: “The emperor’s new clothes”?
This clothes is made of
QCD vacuum. Intelligent
people see a splendid
structure. Stupid people see nothing!
Selling for one million dollars!
Wonderful! I buy it.
Great! We have
produced GDP of one million
dollars!
Demonstration with a key issue:Quantum Lorentz Invariance with
Tensor Gauge Coupling
Lorentz Invariance of Quantum Gravity
Two keywords in modern physics
• Quantization (量子化 )
• Symmetry (对称性 ) 1) Space-time symmetry
2) Gauge symmetry
Classical Lorentz Invariance
Four-vector gauge field
Quantum Lorentz Invariance
Clarification on Lorentz Covariance
1 1T. Goldman et al.: using (1,0) (0,1) instead of ( , )
2 2
Two approaches towards quantum Lorentz Invariance in gauge theory
• Covariant quantization with non-physical states
• Physical quantization with non-covariant propagator
Electrodynamics: vector gauge coupling
• Covariant quantization with non-physical states: Gupta-Bleuler
• Physical quantization with non-covariant propagator: Coulomb gauge
The non-covariant propagator of Physical photon
A delicate point: the contact term and its effect
Cancelation of the contact term
The fortune of Abelian gauge theory: Uniqueness of Coulomb gauge
Gravitation as tensor gauge coupling
The physical graviton propagator
Propagator of general gauge field
The contact term and its effect
Choice of tensor gauge conditions: Non-uniqueness
Hamiltonian in various gauges
Test for Quantum Lorentz Invariance!
Thank you!谢谢 !