Abstract
We consider a system, consisting of a metric tensor , a scalar field , a Weyl's gauge field and a scalar matter field , 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 is considered in a gauge-independent manner. We point out that in a correct treatment where 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.
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