  We study the perturbative quantization of 2-dimensional massive scalar field
theory with polynomial (or power series) potential on manifolds with boundary.
We prove that it fits into the functorial quantum field theory framework of
Atiyah-Segal. In particular, we prove that the perturbative partition function
defined in terms of integrals over configuration spaces of points on the
surface satisfies an Atiyah-Segal type gluing formula. Tadpoles (short loops)
behave nontrivially under gluing and play a crucial role in the result.
