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We study the d - dimensional Bose gas at finite temperature using therenormalization group method. The flow - equations and the free energy havebeen obtained for dimension d, and the cases d<2 and d=2 have been analysed inthe limit of low and high temperatures. The critical temperature, the coherencelength and the specific heat of a two dimensional Bose gas have been obtainedusing a solution for the coupling constant which does not present a singularbehavior.Comment: 18 page

Renormalization-group analysis of the dilute Bose system inddimensions at finite temperature