Propagator-cancelling scalar fields

We examine a large class of scalar quantum field theories where vertices are able to cancel adjacent propagators. These theories are obtained as diffeomorphisms of the field variable of a free field. Their connected correlations functions can be computed efficiently with an algebraic procedure dubbed connected perspective in earlier work. Specifically, (1) We compare the Feynman rules in momentum-space to their position-space counterparts, they agree. This is a a-posteriori justification for the Feynman rules of the connected perspective. (2) We extend the connected perspective to also incorporate counterterm vertices. (3) We examine a specific choice of diffeomorphism that assumes the vertices at different valence proportional to each other. We find that these relations lead to various simplifications. (4) We perturbatively compute the connected 2-point function to all orders for an arbitrary diffeomorphism of a massless field. We thereby give a systematic perturbative derivation of the exponential superpropagator known from the literature. (5) We compute a number of one- and two-loop counterterms. We find that for the specific diffeomorphism, the one-loop counterterms arise from the bare vertices by a non-linear redefinition of the momentum. (6) We show that every diffeomorphism fulfils a set of infinitely many Slavnov-Taylor-like identities which express diffeomorphism-invariance of the S-matrix at loop-level. Finally, we comment on surprising similarities between the structure of propagator-cancelling scalar theories and gauge theories .