Finite number and finite size effects in relativistic Bose-Einstein condensation

Bose-Einstein condensation of a relativistic ideal Bose gas in a rectangular cavity is studied. Finite size corrections to the critical temperature are obtained by the heat kernel method. Using zeta-function regularization of the one-loop effective potential, lower-dimensional critical temperatures are calculated. In the presence of strong anisotropy, the condensation is shown to occur in multisteps. The criteria of this behavior is that critical temperatures corresponding to lower-dimensional systems are smaller than the three-dimensional critical temperature.