ϕϵϕϵ-Coordinated modules for vertex algebras

We study ϕϵϕϵ-coordinated modules for vertex algebras, where ϕϵϕϵ with ϵ   an integer parameter is a family of associates of the one-dimensional additive formal group. As the main results, we obtain a Jacobi type identity and a commutator formula for ϕϵϕϵ-coordinated modules. We then use these results to study ϕϵϕϵ-coordinated modules for vertex algebras associated to Novikov algebras by Primc.