Introduction
Conformal field theory is a quantum field theory invariant under conformal (angle-preserving) transformations, which powerfully constrains correlation functions and often makes theories exactly solvable, especially in two dimensions. It underpins string worldsheet dynamics and captures universality classes at critical points in statistical and condensed matter systems.
Contents
Virasoro Algebra
Witt Algebra and Virasoro Algebra
Unitary Highest Weight Representations
The Verma Module
The Integrability Theorem
Loop Groups
Vertex Operator Algebra
The Semigroup of Annuli
The Semigroup of Annuli
Conformal Welding Problem
The Fock Model
The Fock Space
Symplectic Hilbert Spaces
The Weil Representation
Embed Into The Semigroups