“A gauge field describes two dynamical degrees of freedom of a massless spin-1 particle. A most economic description would have been using a two component field. However, to have Lorentz symmetry, one has to imbed the two degrees of freedom into a four-vector field 'A', thereby introducing the gauge degrees of freedom. To ensure the gauge part do not contribute to physical observables, manifest gauge symmetry is required. The gauge degrees of freedom seem to be a nuisance, it would be nice to get rid of them in actual calculations. However, this can only be done by first formulating a Lorentz-invariant theory and then imposing gauge conditions. The order of the procedure here is critically important and cannot be reversed: one cannot construct physical observables directly in term of “physical” degrees of freedom after imposing the gauge conditions. Reversely-engineered gauge symmetry is not guaranteed physical because 1) observables generally do not have proper Lorentz transformation, 2) they generally are non-local, 3) they generally have no physical measurements.”[X. Ji, Phys. Rev. Lett. 106, 259101 (2011) [arXiv: 0910.5022 [hep-ph]].
In the attached paper, a pure Yang-Mills gauge theory has been completely defined in Hamiltonian formulation with the help of the generalized Coulomb gauge – a null covariant derivative which not only has Lorentz symmetry (i.e., by definition, in terms of a co-ordinate system the covariant derivative of a ‘vector’ transforms under a change of co-ordinate system ‘in the same way’ as the ‘vector’ itself) at the first instance but also, at the same time, imposes gauge fixing condition in Equation (8) of the attached paper. Moreover, non-abelian Gauss law in Equation (4) of the attached paper is covariant with respect to the Lorentz transformations, so, the generalized Coulomb gauge term as part of this non-abelian Gauss law is also covariant with respect to the Lorentz transformations. Thus, the aforesaid order of procedure has been strictly followed in the Hamiltonian formulation of the attached paper. Consequent upon the same, Ak┴, the two “physical” degrees of freedom in the Hamiltonian formulation of the attached paper, are physical enough in the laboratory inertial reference frame such that any thing made out of it is ‘directly’ physical. The simplest gauge-invariant ‘physical observable’ to be made out of Ak┴, the two “physical” degrees of freedom, is gluon helicity, defined as the projection of gluon spin operator along the direction of the momentum.
Accordingly, based on the aforesaid physical observable 'gluon helicity', the Gribov copies has been theoretically predicted and experimentally confirmed as physical entities on the basis of earlier published experimental paper “G. Alexander et al. (OPAL Collaboration), “Measurement of three-jet distributions in e +e- annihilations at sq. root s= 91 GeV sensitive to the gluon spin”, Z. Phys. C - Particles and Fields 52, 543-550 (1991)” in the attached paper.
Conference Paper Existence of Mass-Gap & Pure Yang – Mills Theory (Final Vers...
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