Effective field theory approach to the weakly interacting bose gas

In this paper we study the theory of nonrelativistic weakly interacting Bose gas from the point of view of effective field theory. Firstly, the nonrenormalizability of the theory is briefly discussed. Then, starting from the effective Lagrangian, the lowest order contributions of Feynman diagrams are calculated for the parameters in the effective Lagrangian. These illustrate the running coupling constant phenomenon. After that, the differential align of the parameters in the effective Lagrangian is obtained. We show that the intrinsic energy scale of this effective theory can be removed, while it is not possible to do so for relativistic Bose gas. Our results can help to study the critical behavior of weakly interacting Bose gas.