  Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using
a family of $SO(3)$-equivariant differential $^*$-representations. The
quantization maps are determined from the combination of the Wigner theorem for
$SU(2)$ with the polar decomposition of the quantized plane waves. A tracial
star-product, equivalent to the Kontsevich product for the Poisson manifold
dual to $\mathfrak{su}(2)$ is obtained from a subfamily of differential
$^*$-representations. Noncommutative (scalar) field theories free from UV/IR
mixing and whose commutative limit coincides with the usual $\phi^4$ theory on
$\mathbb{R}^3$ are presented. A generalization of the construction to
semi-simple possibly non simply connected Lie groups based on their central
extensions by suitable abelian Lie groups is discussed.
