Structure of the Yang - Mills Vacuum in Coulomb Gauge

The non-uniqueness of Yang-Mills potentials in the Coulomb gauge leads to a non-trivial vacuum structure featuring vacuum fields of both integer and half-integer topological charge. Instantons fit in consistently with this picture and their interpretation is not changed. Integer and half-integer vacua are connected by certain meron solutions and the existence of half-integer charged states appears to be important for the confinement properties of the theory. (Submitted to Phys. Letters. ) * Work supported by Department of Energy 2 The discovery of instanton solutions to the Yang-Mills field equations [I] has revealed an interesting structure of the Yang-Mills vacuum [2]. This vacuum structure is most easily seen in A0 = 0 gauge [2] and arises from the non-uniqueness of vacuum-field potentials in this gauge. More recently, Gribov [3] has pointed out that non-uniqueness of Yang-Mills potentials occurs even in the more restrictive Coulomb gauge, a so-called physical gauge. In this note, we study the Yang-Mills vacuum in Coulomb gauge and find that Gribovts non-uniqueness leads to a nontrivial vacuum structure featuring vacuum potentials with both integer and halfinteger topological charge. We find a similar non-uniqueness in the gauge transformation which takes the instanton solution into Coulomb gauge and correlate this to our Coulomb gauge vacuum structure. The existence of half-integer charged vacuum fields does not change the effects of instantons in the theory, but rather is related to the presence of meron solutions of the field equations. Recently it has been realized by various authors that half-integer charged field configurations are those which are relevant to the confining properties of the theory. These fields give rise to a large Wilson vacuum-integral[4,5] or a confining Coulomb force [3,6] . We begin with a description of vacuum fields for SU(2) Yang-Mills theory in the Coulomb gauge. We will characterize these fields by the value of the topological charge l-1 tl =24n2 d3x f ijk In the Coulomb gauge a vacuum-field potential AP is a pure gauge (1) ;= U-‘TV, A0 = 0 (2) satisfying the condition