  On the basis of the general principles of a gauge field theory the gauge
theory for the Poincar\'{e}-Weyl group is constructed. It is shown that tetrads
are not true gauge fields, but represent functions from true gauge fields:
Lorentzian, translational and dilatational ones. The equations of gauge fields
which sources are an energy-momentum tensor, orbital and spin momemta, and also
a dilatational current of an external field are obtained. A new direct
interaction of the Lorentzian gauge field with the orbital momentum of an
external field appears, which describes some new effects. Geometrical
interpretation of the theory is developed and it is shown that as a result of
localization of the Poincar\'{e}-Weyl group spacetime becomes a Weyl-Cartan
space. Also the geometrical interpretation of a dilaton field as a component of
the metric tensor of a tangent space in Weyl-Cartan geometry is proposed.
