towards a final criteria of separating momentum and angular momentum outline: i.the matter of...
DESCRIPTION
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 I. The matter of convenience and fine-tuning in actual applicationTRANSCRIPT
Towards a final criteria of separating momentum and
angular momentum
Outline:I.The matter of convenienceII.The matter of reasonablenessIII.The matter of correctness
Xiang-Song ChenHuazhong University of Science & Technology
陈相松 •华中科技大学•武汉16 Feb 2012 @ INT-Seattle
Recall of the Controversies
t3 3 3 3
3 3
otal
tota3
l
Jaffe-Manohar [NPB337:509 (1990)]
Ji [PRL78:610 (1997)], Chen-Wang [CTP27:
1 12
1212 (1997)]
Chen
12
-Lu-S
i id x d x dx E A x E Ai
x D x E B
J x d x
d x d x d xi
J
3 3pure phys pure phy
3 3total s
t
un-Wang-Goldman [PRL100:232002 (2008); 103:062001 (2009)]
Wakamatsu [PRD81:114010(2010); 83:014012 (2011); 84:037501
1 1 D2
(2011)]
i ix D E A x E Ai
d x x dJ
J
d x d x
3 3phys pure potal hys phys
3 31 1 ( D )2
i i a ax D E A x Ed x d x d x di
x A A
Leader [PRD 83:096012 (2011)]
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
I. The matter of convenience and fine-tuning in actual application
Hint from a forgotten practice: Why photon is ignored for atomic spin?
Do these solutions 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 – Angular Momentum
Gauge-invariant revision-Momentum and Hamiltonian
The covariant scheme
spurious photon angular momentum
Gluon angular momentum in the nucleon:
Tree-level
0
)( ' 3
BErxdJ g
One-gluon exchange has the same property as one-photon exchange
Beyond the static approximation
Fine-tuning for the gluon spin and OAM
Possible convergence in evolution
Leader’s compelling criteria to remove the controversy Recalling the Poincare algebra and subalgebra for and interacting systemGenerators for the physical fields: QEDThe quark-gluon system
II. The matter of reasonableness ---Leader’s criteria of separating
momentum and angular momentum
The controversy and Leader’s Criteria
p
3 3 3 3
3 3ure
total
to3
tal
Jaffe-Manohar [NPB337:509 (1990)]
Chen-Lu-Sun-Wang-Goldman [PRL100:232002 (2008); 103:062001 (2009)]
1 12
1 12
i iJ
J
d x x E A xd x d x E Ai
x Di
d x
d x d x d
phys pure phys
p
3
3 3hys pure phys phto
3ys
3tal
Wakamatsu [PRD81:114010(2010); 83:014012 (2011); 84:037501 (
D
1 1 ( D
2011)]
)2
i i
i i a a
E A x E A
x D E
x d x
d x d x d x d xA Ai
J x E A
Interacting theory: Structure of Poincare generators
int
i t
n
n
i t
"bad" genera Lagrangian:
Spatial translation and rotation are
"Good" generators
kine
tors
a b
a b
a b
a
a b
b
P P PJ
H = H H HK K KJ KJ
L L L L
Time translation and Lorentz boost ar dmatic
e ynamic
Interacting theory: Poincare (sub)algebra
( , ) ( , )
( , ) ( , )
( ,
,
)
,
, ,
[ , ]Kinematic transformation [ , ]
[ , ] 0
[ , ]Dynamic transformat
Only total
ion [ , ]
and are
i j ka
i j ka b ijk
b ijk a bi j k
a b ijk
a bi
a b
ja b a b ij
i ja b
K J i KK P
J
J J i JJ P i PP
i
P
H
P
[ , ] covariant:
[ , ]
i j kijk
i jij
K J i KK P iH
Generators for the gauge-invariant physical fields - translation
Generators for the gauge-invariant physical fields - Rotation
The quark-gluon system
Generator for the gauge-invariant quark field
Generator for the gauge-invariant gluon field
Some detail in the proof
III. Possibly a real final solution
i iE A E x A
Dipole rad.
11
ikreB LYikriE B i Ak
(rad. gauge)
l=1
m=1
E B 21 cosdP
d
E Flux
J Flux
x E B
21 coszdJd
22sinzdJd
Miracle of quantum Measurement
A system can only be detected in
certain eigenstate
E.g. Optical pumping of a trapped ion
The issue of “indirect” observable in QCD: matter of
definition, but …The same experiments as to
“measure” the conventional PDFsNew factorization formulae and
extraction of the new PDFsQuark and gluon orbital angular
momentum can in principle be measured through generalized (off-forward) PDFs
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)
Conditions Results
Need for the physical variable:
Real emergence of a photon
Thank you!谢谢 !