  Two-particle correlations are a widely used tool for studying relativistic
nuclear collisions. Multiplicity fluctuations comparing charge and particle
species have been studied as a possible signal for Quark-Gluon Plasma (QGP) and
the QCD critical point. These fluctuation studies all make use of particle
variances which can be shown to originate with a two-particle correlation
function. Momentum correlations and covariances of momentum fluctuations, which
arise from the same correlation function, have also been used to extract
properties of the nuclear collision medium such as the shear viscosity to
entropy density ratio, the shear relaxation time, and temperature fluctuations.
Searches for critical fluctuations are also done with these correlation
observables. We derive a mathematical relationship between several number and
momentum density correlation observables and outline the different physics
mechanisms often ascribed to each. This set of observables also contains a new
multiplicity-momentum correlation. Our mathematical relation can be used as a
validation tool for measurements, as a method for interpreting the relative
contributions of different physics mechanisms on correlation observables, and
as a test for theoretical and phenomenological models to simultaneously explain
all observables. We compare an independent source model to simulated events
from PYTHIA for all observables in the set.
