Advanced Quantum Field Theory: intuition with path integrals

Master Quantum Field Theory and Renormalization group with Path Integrals: Intuitive Insights & Practical Applications

What you'll learn
- Master Path Integrals: Understand the concept of path integrals in Quantum Field Theory, and learn how they offer a unique perspective on the subject
- Derive Feynman Rules: Gain the ability to derive Feynman rules naturally from the path integral formulation
- Dive into Renormalization: Delve into the essential concept of renormalization, with a particular focus on the renormalization group.
- Comprehend Non-Commutativity: Explore the non-commutative nature of Quantum Field Theory by examining how path integrals incorporate non-differentiable paths
- Derive the Yukawa potential: while discussing renormalization, we will see how some theories give rise to long-range potentials and some others short-range ones
- Discover the partition function: essential tool to the definition of path integrals
- Learn how to use correlation functions, whose interpretation is related to Feynman diagrams and particle interactions
- Learn how to use perturbation theory in QFT
- Learn the orbit-stabilizer theorem, another key concept related to the interpretation of Feynman diagrams
- Discover the effective action: this tool is key to understanding renormalization
- Discover the Callan Symanzik equation, which appears in the theory of the renormalization group
- Learn why "anomalous" dimensions arise in QFT

Requirements
- Schrödinger equation
- Operators, states, eigenstates, eigenvalues
- familiarity with bra-ket notation
- Classical theory of Fields (Lagrangian, action, etc)
- Multivariable Calculus
- Complex calculus (in particular, the Residue Theorem)
- Familiarity with QFT and second quantization will enhance your learning experience
- Special Relativity (and tensors)

Description
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. Explore the intricacies of the renormalization group, a fundamental aspect of Quantum Field Theory.

Course Content:the current course content covers path integrals, zero-dimensional QFT, one-dimensional QFT, and renormalization. The material may be expanded in the future to include additional sections.

Prerequisites:To fully benefit from this course, it's essential to have a grasp of:

Schrödinger equation

operators

bra-ket notation

multivariable calculus and complex calculus

Classical Theory of fields

Special Relativity and tensors

Familiarity with QFT and second quantization will enhance your learning experience.

Enroll today and embark on a captivating journey into the heart of Quantum Field Theory. Discover the power of path integrals and develop a deep, intuitive understanding of this fascinating field. Join this course to reshape your perspective on Advanced Quantum Field Theory!

Who this course is for:
- Advanced (Master-level) Students
- Physicists and Researchers: Professionals in the field of theoretical physics, including physicists, researchers, and academics, who wish to enhance their expertise in Quantum Field Theory.
- Mathematics Enthusiasts, Mathematicians, interested in the intersection of advanced mathematics and theoretical physics, looking to explore the beauty of Quantum Field Theory from a mathematical perspective.
- Physics Enthusiasts, passionate about the world of quantum physics and eager to deepen their understanding of Quantum Field Theory.
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