  We examine in detail two alternative descriptions of a system of $\alpha$
particles interacting via local interactions of different character,
highlighting the fact that a faithful microscopic description of such systems
demands a consistent treatment of both short- and long-range correlations. In
preparation, we examine four different versions of modern microscopic many-body
theory and conclude by emphasizing that these approaches, although {\it a
priori} very different, actually lead to the same equations for their efficient
application. The only quantity that depends on the formulation of many-body
theory chosen is an {\it irreducible} interaction correction. In the language
of Green's functions and Feynman diagrams, it is the set of both
particle-particle and particle-hole irreducible diagrams, and in variational
Jastrow-Feenberg theory it is determined by {\it multipartite correlations} and
{\it elementary diagrams}. We apply these theoretical methods to the
calculation of the energetics, structure, thermodynamics, and dynamics of
$\alpha$ matter, as well as its condensate fraction. In dimensionless units,
$\alpha$ matter appears to be remarkably similar to the much-studied $^4$He
quantum fluid, its low-temperature properties now basically solved in the
Jastrow-Feenberg framework. Accordingly, one can have confidence in the results
of application of the same procedure to $\alpha$ matter. Even so, closer
examination reveals significant differences between the physics of the two
systems. Within an infinite nuclear medium, alpha matter is subject to a
spinoidal instability. Extended mixtures of nucleons and alpha particles are
yet to be given rigorous consideration in a corresponding theoretical
framework.
