The prevailing theoretical quark and gluon momentum,orbital angular momentum and spin operators,satisfy either gauge invariance or the corresponding canonical commutation relation,but one never has these operators which satisfy both except the quark spin.The conflicts between gauge invariance and the 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 gauge invariance and canonical momentum and angular momentum commutation relation,are proposed.To achieve such a proper decomposition the key point 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.
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.
