On Behavior of Weyl's Gauge Field

We consider a system, consisting of a metric tensor g_μv, a scalar field Φ, a Weyl's gauge field A_μ and a scalar matter field Φ, which is invariant under general coordinate transformation and Weyl's gauge transformation. Two kinds of identities and field equations are given and discussed. A special space-time with g_μv = Φ_-2η_μv is considered in a gauge-independent manner. We point out that in a correct treatment where g_μv is not regarded as an independent variable, an auxiliary condition for Weyl's gauge field cannot be obtained. Therefore Weyl's gauge field can be treated as a usual field.