Poincare sub-algebra and gauge invariance in nucleon structure Xiang-Song Chen Huazhong University of Science & Technology 陈相松 •华中科技大学•武汉 10 July 2012 @ KITPC-Beijing
Outline Controversy in nucleon (spin) structure Elliot Leader’s criteria of separating momentum and angular momentum Reconciling Poincare sub-algebra with gauge invariance A practical thinking about nucleon structure A critical thinking about gauge invariance
A universally correct statement for the nucleon spin Nucleon spin comes from the polarization and orbital motion of quarks and gluons --- Chairman Mao
Controversy in nucleon spin structure Leader [PRD 83:096012 (2011)]
Interacting theory:Structure of Poincare generators Without gauge symmetry, the issue is trivial:
Further criteria by Elliot Leader Corollary
Examination of various decompositions by Leader’s criteria Leader [PRD 83:096012 (2011)]
A practical thinking about nucleon structure • Hint from a forgotten practice: Why photon is ignored for atomic spin? • The fortune of choosing Coulomb gauge • Quantitative differences • Another example: momentum of a moving atom and nucleon
Hint from a forgotten practice: Why photon is ignored for atomic spin? Do these solutions make sense?!
Close look at the photon contribution The static terms!
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 One-gluon exchange has the same property as one-photon exchange
Momentum of a moving atom A stationary electromagnetic field carries no momentum
Weinberg’s approach: derivation of QED with physical photons S. Weinberg, Phys. Rev. 138 (1965) B988
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） Need for the physical variable: Real emergence of a photon
A possible real difference Dipole rad. (rad. gauge) l=1 m=1 E Flux J Flux
If we never need physical gluons …… Then QCD is a true gauge theory, and the only try gauge theory so far known And all quark and gluon quantities are a matter of definition
Do we sometimes need physical gluons? Probably, in early universe Then color gauge invariance may also be an illusion!
Derivation of QED with physical photons by requiring Lorentz invariance Derivation of non-Abelian gauge theory with physical gluons by requiring Lorentz invariance???
Summary Nucleon spin and momentum can be separated gauge invariantly, with quark/gluon part acting as the rotation and translation generators for the physical quark/gluon field. If adopting the naive free-form expression, Coulomb gauge gives the simplest pictures for atomic and nucleon structure. Gauge symmetry might be an illusion. QED can be derived from physical photons by requiring Lorentz invariance of S matrix, but the situation for non-Abelian theory is more tricky and not yet proven. demonstrated.
Thank you! 谢谢!