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We discuss the equilibrium properties of dilute Bose gases using anon-perturbative formalism based on auxiliary fields related to the normal andanomalous densities. We show analytically that for a dilute Bose gas ofweakly-interacting particles at zero temperature, the leading-order auxiliaryfield (LOAF) approximation leads to well-known analytical results. Close to thecritical point the LOAF predictions are the same as those obtained using aneffective field theory in the large-N approximation. We also report analyticalapproximations for the LOAF results in the unitarity limit, which comparefavorably with our numerical results. LOAF predicts that the equation of statefor the Bose gas in the unitarity limit is E / (p V) = 1, unlike the case ofthe Fermi gas when E / (p V) = 3/2.

Analytical limits for cold atom Bose gases with tunable interactions