Critical Temperature of Dilute Bose Gases

We compute the critical temperature of Bose-Einstein condensation in dilute three-dimensional homogeneous Bose gases. Our method involves the models of spatial permutations and it should be exact to lowest order in the scattering length of the particle interactions. We find that the change in the critical temperature is proportional to a rho^{1/3} with constant c = -2.33; this contradicts the current consensus among physicists.

💡 Research Summary

The paper tackles a long‑standing problem in the theory of dilute Bose gases: how weak interparticle interactions shift the Bose‑Einstein condensation (BEC) temperature relative to the ideal‑gas value. In the non‑interacting case the critical temperature (T_{c}^{0}) is determined solely by the particle density (\rho) and the mass (m). When a finite s‑wave scattering length (a) is introduced, many theoretical approaches—effective‑field theory, renormalization‑group analyses, and large‑scale path‑integral Monte‑Carlo simulations—have converged on a positive linear shift, \