  It is unavoidable to deal with the quark and gluon momentum and angular
momentum contributions to the nucleon momentum and spin in the study of nucleon
internal structure. However, we never have the quark and gluon momentum,
orbital angular momentum and gluon spin operators which satisfy both the gauge
invariance and the canonical momentum and angular momentum commutation
relation. The conflicts between the gauge invariance and canonical quantization
requirement of these operators are discussed. A new set of quark and gluon
momentum, orbital angular momentum and spin operators, which satisfy both the
gauge invariance and canonical momentum and angular momentum commutation
relation, are proposed. The key point to achieve such a proper decomposition is
to separate the gauge field into the pure gauge and the gauge covariant parts.
The same conflicts also exist in QED and quantum mechanics and have been solved
in the same manner. The impacts of this new decomposition to the nucleon
internal structure are discussed.
