Remarks on Lattice Gauge Fixing

In the lattice gauge theories where the links belong to a compact group, the gauge fixing is necessary only in the case of the measure of a gauge dependent operator. An expression similar to (1) but without having gauge fixed the links, defines the expectation value of a gauge independent operator. Moreover, in a lattice simulation there is no need to compute the Faddeev-Popov determinant because the correct adjustment of the measure, necessary in the case of gauge fixing, is obtained rotating the links in the chosen gauge. Therefore the complexity of the ghost technique is replaced by the numerical evaluation of the gauge transformations. The price to pay is the large amount of computer time spent to obtain numerically the gauge transformations. From a numerical point of a view the values of a gauge dependent operators strongly fluctuate around zero if the gauge has not been fixed. In the case of an imperfect or inadequate gauge fixing the measure of a gauge dependent operator is affected by additional fluctuations to be summed up to the intrinsic statistical noise. The necessary steps bringing to the computation of the integral (1) can be described as follows: