Transition Temperature of a Homogeneous and Dilute Bose Gas Between Two and Three Dimensions

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The phase transition temperature of a homogeneous and dilute Bose gas in the short-wavelength range and in D-dimensions (2 < D ≤ 3) is calculated by using a mean-field-based method of statistical physics. The shift of the phase transition temperature is written to the leading order as ∆Tc/T 0 c = cγ , where γ = na. We derive Huang’s result for the phase transition temperature in generalized dimensions. We show that c(D) is positive and α(D) = 2(D/2 − 1) in the shortwavelength range. The origin of the difference between α = 1/2 and α = 1 at D = 3 is discussed.