Conformal Field Theory

Conformal field theory studies quantum fields whose symmetries include conformal transformations. Its examples connect local operators, correlation functions, representations of symmetry algebras, and the geometry of the spaces on which the theory is defined. This collection separates the mathematical structures used to formulate a model from the physical assumptions that identify its observables and interpretation. Definitions fix conventions before statements use them, and examples show how those conventions enter calculations.

The pages develop selected aspects of conformal models and their relation to the surrounding quantum-field and string-theory material. Mathematical prerequisites are linked explicitly so that algebraic identities, analytic arguments, and physical postulates can be read with their proper roles. Results about a specified mathematical model do not by themselves establish that the model describes a particular experiment. Reading the development pages together with their example companions helps keep those distinctions visible. The dependency links provide routes back to the representation theory, geometry, and field-theoretic constructions on which individual arguments rely.