Tensor network techniques have been crucial to study strongly coupled spin systems. The application of these techniques to quantum fields presents the challenge of dealing with infinite dimensional systems. Inspired on standard field theory techniques, we propose a new strategy based on preserving the continuum character of fields and use them as building blocks of an adapted Tensor Renormalization Group protocol. Its viability is tested by evaluating the partition function of a free massive boson on a 2D square lattice and a phi^4 theory at first order in the coupling constant. The Boltzmann weights of the free lattice model are shown to satisfy the Yang-Baxter equation with a uniformization given by trigonometric functions in the massless case, and Jacobi elliptic functions in the massive case. A related factorizable S-matrix model for continuous degrees of freedom is constructed. These results place the free boson in 2D in the same position as all other models that are exactly solvable `a la Yang-Baxter.