  The decomposition of 4-point correlation functions into conformal partial
waves is a central tool in the study of conformal field theory. We compute
these partial waves for scalar operators in Minkowski momentum space, and find
a closed-form result valid in arbitrary space-time dimension $d \geq 3$
(including non-integer $d$). Each conformal partial wave is expressed as a sum
over ordinary spin partial waves, and the coefficients of this sum factorize
into a product of vertex functions that only depend on the conformal data of
the incoming, respectively outgoing operators. As a simple example, we apply
this conformal partial wave decomposition to the scalar box integral in $d = 4$
dimensions.
