Nucleon Momentum and Spin Decompositions

Abstract

We construct a gauge invariant canonical momentum operator which satisfies the canonical commutation relation to resolve the old controversy on the canonical versus kinematic momentum of a charged particle in gauge theories. With this we show how to obtain the gauge independent momentum and spin decompositions of composite particles to those of the constituents in QED and QCD, which has been thought to be impossible. Moerover, we show that there are two logically acceptable nucleom momentum and spin decompositions, depending on which gluons we identify as the constituent of nucleons.