Gauge Invariance, Lorentz Covariance and Canonical Quantization in Nucleon Structure Studies

Different operators of quark and gluon momenta, orbital angular momenta, and gluon spin have been used in nucleon structure studies. Their precise meaning is reviewed with respect to gauge invariance, Lorentz covariance and canonical quantization rules. The advantage and disadvantage of different definitions are analyzed. We concentrate on our gauge invariant decomposition of the total momentum and angular momentum into quark and gluon parts based on the separation of the gauge potential into a gauge invariant (covariant) physical part and a gauge dependent pure gauge part. The Lorentz covariance and measurability of our operators are demonstrated.