We show that the critical temperature of a uniform dilute Bose gas increases linearly with the $s$-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

• Received 1 June 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.1703