In this talk we consider the polymer measure with selfinteractions, which is called the Edward model. The two-dimensional case had been studied around 2000, and the polymer measure and the associated Dirichlet form were constructed. Here, we consider the three-dimensional case, which requires harder calculation than the two-dimensional case. It is known that, to construct the measure we need the renormalization, because of the singularity of the interactions. Moreover, the renormalization constant coincides with that of the $\Phi ^4$-quantum field measure. In this talk, I will explain the strategies to construct the measure and the Dirichlet form.

This talk is based on jointworks with Sergio Albeverio, Makoto Nakashima and Song Liang.