Reply to the comment of Huey-Wen Lin and Keh-Fei Liu on "Controversy concerning the definition of quark and gluon angular momentum" by E. Leader (arXiv:1111.0678, PRD 83, 096012 (2011))

Abstract: Lin and Liu evaluate the nucleon expectation value of the non gauge-invariant canonical quark momentum operator on a lattice, and obtain zero. They conclude that my argument that, despite the non gauge-invariance of the operator, its physical matrix elements \emph{are} gauge-invariant, cannot be correct. I show that their result has no bearing on the question of gauge-invariance, and also point to an amusing lattice paradox.