Conformal Transformations: Symmetries and Correlation Functions

This lecture delves into the intricacies of conformal transformations, focusing on the preservation of distances and angles. The discussion covers the significance of conformal symmetry in quantum field theory, emphasizing the invariance of correlation functions under transformations. The instructor elucidates the implications of conformal covariance and the role of scaling operators in conformal field theories. By exploring the transformation laws for different types of operators, including scalar primaries and spinning operators, the lecture unveils the fixed nature of correlation functions in conformal theories. Furthermore, the lecture delves into the constraints imposed by dilatations, inversions, and translations on correlation functions, shedding light on the structure of correlation functions in conformal field theories.