# Problems related to gauge invariance, Lorentz covariance and canonical quantization applied to the study of nucleon structure

**Fan Wang**

Nanjing University

I will show that the polarized deep inelastic scattering measured quark spin contribution to nucleon spin can be understood within the constituent quark model. The proton spin crisis is due to misidentification of the nonrelativistic Pauli spin operator with the relativistic quark axial vector current operator. Ji's present decomposition is unphysical, because the quark orbital angular momentum does not satisfy the standard angular momentum algebra. The corresponding momentum components do not commute and so can not be used to describe the 3-dimensional quark momentum distribution. A new decomposition of the momentum and angular momentum of gauge systems is shown to be both gauge invariant, Lorentz covariant and to satisfy the canonical commutation relation. The massless photon and gluon both have their spin and orbital angular momentum and the measured gluon spin is the matrix element of this gluon spin operator in the infinite momentum frame. The measured quark momentum parton distribution is the matrix element of the gauge invariant canonical momentum operator in the infinite momentum frame.