Research On Weak Locality Of Field Algebra And Quotient Space

In this paper,firstly,definitions and related conclusions of state field correspondence are recalled.Secondly,formal definitions and related results of field algebras and vertex algebras are given,and an example that satisfies the weak locality of field algebras,but does not satisfy the locality of vertex algebras is constructed to compare the weak locality and the locality of the operator.We investigate the weak locality of field algebras in detail in order to understand the weak locality of field algebras.Finally,the quotient space of field algebras is obtained by its bilateral ideals.And some theorems on the quotient space of field algebras are explored.This paper is divided into five portions.In the first portion,we explain the research background and current status of the content of this article.In addition,we introduce the corresponding domestic and foreign developments,and also elaborate the significance of research on the issues involved in this article.In the second portion,the related concepts and conclusions of the state field correspondence are reviewed,and the properties of state field correspondences are discussed.In the third portion,the related basic concepts and related results of field algebras and vertex algebras are reviewed.An example that satisfies weak locality,but does not satisfy locality,is constructed.And the weak locality of field algebras is studied in some detail.In the fourth portion,we explore some basic properties of field algebraic quotient spaces.In the last portion,the main content of this paper is summarized.