ar X iv : h ep - p h / 92 06 25 3 v 2 1 S ep 1 99 2 NUB 3053 / 92 Wightman Functions in QCD

The constraint imposed by Gauss' law is used to show that the matrix elements of n-point Wightman Functions of gluon field and quark current operators at different space time points vanish when taken between physical states. – 2 – 1. Introduction. Christ and Lee[1,2] have warned against the common practice of starting from a formal path integral approach prior to choosing a gauge. In fact, for QCD they chose the (time)-axial (or temporal) gauge[3,4,5] which has a well defined Hamiltonian and then derived the Feynman rules for different gauges by appropriate coordinate transformations. In the temporal gauge, their construction of the path integral generating functional requires for consistency that it operate only between color singlet states. For our purposes it will be convenient to work in the canonical formalism[5]. In section 2 we point out that just implementing the constraints, due to Gauss' law, on physical states in the temporal gauge leads us to a pleasing result: all transition matrix elements of the color electric and magnetic fields as well as of color carrying currents between physical states vanish. This forecloses the possibility of any physical state with non-zero color appearing. In section 3 we show that two point Wightman functions of quark current and gluon fields in physical states vanish when the two points do not coincide, and in section 4 we extend the results to n-point functions.