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

Non-perturbative predictions for cold atom Bose gases with tunable interactions