Renormalization in Perturbative Quantum Field Theories: A View from Kenneth G. Wilson’s Approach (2025)
This work studies gauge theories from a mathematical formulation based on principal fiber bundles, from which the notions of connection and curvature are rigorously constructed, revealing the geometric origin of these theories. Their development is first addressed within the classical framework of fields, that is, prior to quantization, and then the idea of quantization is introduced from the perspective of the path integral, focusing on the perturbative framework, where the problem of redundancies naturally arises and is resolved through the Faddeev–Popov method. Finally, the perspective of Kenneth Wilson on quantum field theories is explored, allowing for the formulation of effective theories through the introduction of a cut-off, following the modern exposition of Kevin Costello.