We develop a theory of φ-coordinated (quasi-) modules for a general nonlocal vertex algebra where φ is what we call an associate of the one-dimensional additive formal group. By specializing φ 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 φ-coordinated modules to a certain quantum βγ-system explicitly.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics