Abstract
A non-uniqueness problem of gauge invariant separation of quark and gluon contributions to nucleon spin is considered. We show that there is a wide number of gauge invariant spin decompositions, and each of them reduces to the canonical one in a special gauge. A class of physical gauge equivalent nucleon spin decompositions is selected by requirements of consistence with helicity notion described within the E(2) little group representation theory and with the gluon helicity Δg measured in the experiment.
Highlights
It has been a long-standing problem of gauge invariant definition of gluon spin and orbital angular momentum [1, 2]
The background field Bμ transforms as a gauge potential whereas the quantum field Qμ transforms as a covariant color vector under the classical type of gauge transformation [13,14]
One can identify the field Bμ with a pure gauge field Apμure and the field Qμ with a physical gauge potential Apμhys by imposing two conditions, Fμν (Apure) = 0, DiApi hys = 0, (6)
Summary
It has been a long-standing problem of gauge invariant definition of gluon spin and orbital angular momentum [1, 2]. The final expression for the gauge invariant decomposition of nucleon spin corresponds to the space vector part of eq (5) [4]. Each term in the decomposition has become gauge invariant due to the covariant transformation law for the physical field Aphys.
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