Color Confinement in Quantum Chromodynamics. II

Abstract

has been imposed on physical states Iphys) on the assumption of the absence of the spontaneous symmetry breaking with respect to the color charge Qa. **) Since the condition (1·2) puts only a constraint on the total color charge of the state Iphys) integrated over the whole three-dimensional space, this condition may not seem to be sufficient for preventing the colored objects from being observed locally. This objection applies to the cases of the charges constituting a symmetry group which is not semisimpleor which allows the existence of local observables behaving nontrivially under it. For instance, in QED having a non-semisimple gauge group U(1), the observation of electrically charged objects is certainly possible in the chargeless state composed of an electron on the earth and a positron behind the moon. In the case of the rotation group SU(2), it is a (semi)simple group, but rotation-group~variant local observables such as angular-momentum density allow us to measure the spin of a particle in the decay products of a spinless particle. Contrary to these cases, the semisimplicity of the color SU(3) and the absence of colored local observables in QCD have been shown in Ref. 1) to protect the colored particles from being observed in the colorless total state satisfying (1' 2). Let Q 1 and Q 2 be spacetime regions spacelikely separated, the former of which is in our side and the