Abstract
The transformation of angular momentum to its Belinfante form requires the smooth behaviour of classical fields at infinity which for the case of quantum operators transforms to the smooth behaviour of matrix elements at small momentum transfers. For the case of quarks this provides the kinematical counterpart of UA(1) problem while for gluons there is a contradiction between kinematics and dynamics governed by Kogut-Susskind pole. This may result in the violation of Equivalence Principle for nucleons or in the stringent constraints to the strange quark polarization in nucleons, while the most likely outcome would be the impossibility to separate gluon angular momentum to spin and orbital parts in the meaningful way.
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