### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 703-741 |

Number of pages | 39 |

Journal | Communications In Mathematical Physics |

Volume | 308 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics