Gauge invariant descriptions of gluon polarizations revisited

Abstract

We examine the feasibility of gauge invariant descriptions of the gluon polarization following the proposal that a gauge field can be decomposed into its physical part and its pure gauge part. We show that gauge invariant angular momentum currents can be constructed from summations of gauge variant Noether currents. We present novel expressions of the pure gauge field, which are used to formulate gauge invariant descriptions of the gluon spin and the photon spin. We show that the gauge invariant extension of the Chern-Simons current can describe the spins of the Laguerre-Gauss laser modes. We also discuss the relation of gauge invariant operators and the parton distributions constructed from Dirac variables.

Gauge invariant descriptions of gluon polarizations

“…We constructed a gauge invariant extension of the Chern-Simons current in section 2, and we verified its gauge-independence in section 4. This extended Chern-Simons current has several remarkable features: It is gauge invariant and is also Lorentz covariant; It satisfies the same equation as the conventional Chern-Simons Current; Furthermore, we shall show that it can describe the spin of the Laguerre-Gauss Laser mode in a subsequent paper [12]. These features support the proposal that it can be considered as an appropriate description of the gluon spin.…”

“…The derivations of gauge invariant decompositions of the angular momentum from the Noether theorem are also discussed in [30] and [31] through different methods. We shall give another derivation from a different perspective in a subsequent paper [12].…”

“…We give some conclusions in section 5. More discussions on the gauge invariant decompositions from the Noether theorem and the extended Chern-Simons current as an appropriate description of the gluon spin will be given in a subsequent paper [12].…”

Reformulations of Yang–Mills theories with space–time tensor fields

“…In the above, we have given the gauge invariant expressions of the SU (2) gluon angular momentum. For another different expression, see [63]. It is interesting to consider whether there exist classical solutions of the Lagrangian In the end of subsection 2.5, we have discussed how to solve e a µ as a function of A a µ .…”