Classification of abstract Bose field models

We classify a class of abstract Bose field models in quantum field theory up to unitary equivalence. The class includes abstract free Bose field models, abstract van Hove–Miyatake models, and infrared-renormalized van Hove–Miyatake models. Moreover, as an application of our classification, we classify quadratic interaction models. In particular, our results answer a question of A. Arai concerning the classification of infrared-renormalized van Hove–Miyatake models.