  We consider cross-spectral purity in random nonstationary electromagnetic
beams in terms of the Stokes parameters representing the spectral density and
the spectral polarization state. We show that a Stokes parameter being
cross-spectrally pure is consistent with the property that the corresponding
normalized time-integrated coherence (two-point) Stokes parameter satisfies a
certain reduction formula. The current analysis differs from the previous works
on cross-spectral purity of nonstationary light beams such that the purity
condition is in line with Mandel's original definition. In addition, in
contrast to earlier works concerning the cross-spectral purity of the
polarization-state Stokes parameters, intensity-normalized coherence Stokes
parameters are applied. It is consequently found that in addition to separate
spatial and temporal coherence factors the reduction formula contains a third
factor that depends exclusively on the polarization properties. We further show
that cross-spectral purity implies a specific structure for the electromagnetic
spectral spatial correlations. The results of this work constitute foundational
advances in the interference of random nonstationary vectorial light.
