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 !