Dotsenko-Fateev Approach: Correlation Functions in Quantum Field Theory

This lecture discusses the Dotsenko-Fateev approach to computing correlation functions in quantum field theory. The instructor begins by reviewing the correlation function in a minimal model, emphasizing the efficiency of the Dotsenko-Fateev method. The lecture covers the introduction of a free Gaussian field and its properties, including the definition of the two-point correlation function. The instructor explains the significance of periodic boundary conditions and the Fourier transform in this context. The discussion progresses to the implications of introducing a background charge and how it modifies correlation functions. The instructor highlights the importance of neutrality conditions and screening operators in determining the richness of the theory. The lecture concludes with a focus on the operator product expansion and the conditions necessary for computing correlation functions in minimal models, illustrating the theoretical framework with examples and emphasizing the mathematical rigor required in quantum field theory.