Advanced Quantum Field Theory: intuition with path integrals

Welcome to "Advanced Quantum Field Theory: Intuition with Path Integrals. " In this course, we take a unique approach to delve deeper into the fascinating world of Quantum Field Theory (QFT). The foundations of this course are based on the notes of Professor David Skinner, although an original perspective will be given, which emphasizes intuition and the power of path integrals.

What You Will Learn:Path Integrals Demystified: Explore Quantum Field Theory from a different angle, using path integrals as our guiding tool. Unlike the traditional "second quantization" approach, we won't begin with a classical field and then transform it into an operator, but rather, we'll start directly from the action and Lagrangian, offering a more intuitive understanding. Summing Over Infinite Paths: In classical field theory, a single trajectory minimizes the action.

Path integrals take us beyond this limitation. You'll grasp the essence of QFT by summing over countless possible paths, gaining insight into the fundamental role of uncertainty. Zero-Dimensional QFT: We'll begin with simpler mathematics in a zero-dimensional QFT, paving the way for a natural derivation of Feynman rules directly from the path integral formulation.

Exploring Non-Commutativity: Delve into the concept of non-commutativity in Quantum Field Theory. Discover how path integrals naturally encompass non-commutative behaviors due to the summation over non-differentiable paths. Renormalization Insights: Gain a deep understanding of renormalization, a crucial concept often overlooked in basic QFT courses.