  In this paper we construct homogeneous star products of Weyl type on every
cotangent bundle $T^*Q$ by means of the Fedosov procedure using a symplectic
torsion-free connection on $T^*Q$ homogeneous of degree zero with respect to
the Liouville vector field. By a fibrewise equivalence transformation we
construct a homogeneous Fedosov star product of standard ordered type
equivalent to the homogeneous Fedosov star product of Weyl type.
Representations for both star product algebras by differential operators on
functions on $Q$ are constructed leading in the case of the standard ordered
product to the usual standard ordering prescription for smooth complex-valued
functions on $T^*Q$ polynomial in the momenta (where an arbitrary fixed
torsion-free connection $\nabla_0$ on $Q$ is used). Motivated by the flat case
$T^* R^n$ another homogeneous star product of Weyl type corresponding to the
Weyl ordering prescription is constructed. The example of the cotangent bundle
of an arbitrary Lie group is explicitly computed and the star product given by
Gutt is rederived in our approach.
