Local and global information and equations with left and right invertible operators in the free Fock space

Abstract

The subject of the work is short description of huge amount of n-point information (n-pi) about the system. Methods for solving equations that satisfy such information are considered. Possible interpretation of left and right invertible operators appearing in these equations is also proposed. For local information, the creation and annihilation operators satisfying the Cuntz relations are introduced. It is also introduced the vector describing the local vacuum which completes the equation for n-pi with a global information. An important components of the work are examples of local operator-valued functions.