$${phi}$$ -Coordinated Quasi-Modules for Quantum Vertex Algebras

We develop a theory of f{phi} -coordinated (quasi-) modules for a general nonlocal vertex algebra where f{phi} is what we call an associate of the one-dimensional additive formal group. By specializing f{phi} to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of Li (Selecta Mathematica (New Series) 11:349–397, 2005). As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum vertex algebras and f{phi} -coordinated modules to a certain quantum βγ-system explicitly.