Advanced Quantum Field Theory: Intuition With Path Integrals
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Advanced Quantum Field Theory: Intuition With Path Integrals
Published 9/2023
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 7.03 GB | Duration: 10h 36m
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 equationoperatorsbra-ket notationmultivariable calculus and complex calculusClassical Theory of fieldsSpecial Relativity and tensorsFamiliarity 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!
Overview
Section 1: Path integrals and Quantum Mechanics
Lecture 1 Introduction to the course
Lecture 2 Course prerequisites
Lecture 3 Path integral derivation
Lecture 4 Some intuition behind the path integral
Section 2: QFT in zero dimensions
Lecture 5 Free field theory in zero dimensions
Lecture 6 The current in the Free field theory in zero dimensions
Lecture 7 Wick theorem as a probabilistic theorem in QFT
Lecture 8 Integrals in perturbation theory
Lecture 9 Example of perturbation theory
Lecture 10 Feynman diagrams from a combinatoric perspective
Lecture 11 Feynman diagrams and orbit stabilizer theorem
Lecture 12 Wilsonian effective action
Lecture 13 Feynman rules with two fields and 4-valent vertices
Lecture 14 Example of action with two fields
Lecture 15 Direct calculation of the effective action without Feynman rules
Lecture 16 Direct calculation of the correlation function without Feynman rules
Lecture 17 How renormalization comes forth
Section 3: QFT in 1 dimension
Lecture 18 QFT in one dimension: action with two fields
Lecture 19 Logarithm of a determinant
Lecture 20 Non-locality of interactions in a one-dimensional Quantum Field Theory
Lecture 21 Non commutativity and path integrals
Lecture 22 Correlation functions and time ordered products
Section 4: Theory of renormalization in physics
Lecture 23 Theory of the renormalization group
Lecture 24 Running of couplings and Callan Symanzik equation
Lecture 25 Anomalous dimensions - part 1
Lecture 26 Anomalous dimensions - part 2
Lecture 27 Scale invariant theories
Lecture 28 Massive scalar field and the Yukawa potential
Lecture 29 Derivation of the Yukawa potential from the Klein Gordon field in 3 dimension
Lecture 30 Renormalization group flow
Lecture 31 The local potential approximation: example on the running of couplings
Section 5: Appendix
Lecture 32 Complex Gaussian integrals
Lecture 33 Lagrange duplication formula
Lecture 34 Relation between Beta and Gamma function
Lecture 35 Derivation of a green function from a differential equation
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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