States and IR divergences in factorization algebras

In field theory, one can consider a variety of states. Within the framework of factorization algebras, one typically works with the natural augmentation state 〈 − 〉aug. In physics, however, other states arise naturally, such as the compactification state 〈 − 〉cptf or the Schwartz state 〈 − 〉Sch, defined by imposing Schwartz boundary conditions. At first sight, the relation among these three states is not obvious. This paper gives a definition of the compactification state in factorization algebras and provides a method for handling infrared divergences in the massless theory. We then prove that the three states are equivalent in both the massive and massless cases.