1302.5152 (Masashi Wakamatsu)

Are there infinitely many decompositions of the nucleon spin ?    [PDF]

Masashi Wakamatsu

We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gage components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions of the nucleon spin. By introducing a constant 4-vector $n^\mu$, which amounts to specifying a Lorentz frame of reference, we explicitly construct a projection operator which projects out the physical component of the gluon, which in turn provides us with a gauge-invariant definition of the gluon spin operator in a seemingly covariant form. This result is then used to verify the gauge- and Lorentz-frame independence of the evolution equation of the longitudinal quark and gluon spins in the nucleon. By drawing on all of these findings together with well-established knowledge from electrodynamics, we argue against the rapidly spreading view in the community that there are infinitely many decompositions of the nucleon spin.

View original: http://arxiv.org/abs/1302.5152