  We derive a theoretical description for dilute Bose gases as a loop expansion
in terms of composite-field propagators by rewriting the Lagrangian in terms of
auxiliary fields related to the normal and anomalous densities. We demonstrate
that already in leading order this non-perturbative approach describes a large
interval of coupling-constant values, satisfies Goldstone's theorem, yields a
Bose-Einstein transition that is second-order, and is consistent with the
critical temperature predicted in the weak-coupling limit by the
next-to-leading order large-N expansion.
