Comment on `Controversy concerning the definition of quark and gluon angular momentum' by Elliot Leader (arXiv:1101.5956, PRD 83, 096012 (2011))

Understand

It is argued by the author that the canonical form of the quark energy-momentum tensor with a partial derivative instead of the covariant derivative is the correct definition for the quark momentum and angular momentum fraction of the nucleon in covariant quantization.

• Although it is not manifestly gauge invariant, its matrix elements in the nucleon will be non-vanishing and are gauge invariant.
• We test this idea in the path-integral quantization by calculating correlation functions on the lattice with a gauge-invariant nucleon interpolation field and replacing the gauge link in the quark lattice momentum operator with unity, which corresponds to the partial derivative in the continuum.
• We find that the ratios of three-point to two-point functions are zero within errors for both the u and d quarks, contrary to the case without setting the gauge links to unity.