Quantum 101

Table of Contents Introduction Historical Context and Significance Foundations of Gauge Theory From U(1) to Non-Abelian Gauge Symmetries Structure of Yang-Mills Fields Lie Groups and Lie Algebras Field Strength Tensor for...

Table of Contents Introduction Historical Background Symmetry in Physics Continuous Symmetries and Conservation Laws Statement of Noether’s Theorem Mathematical Framework Derivation from the Lagrangian Formalism Examples of Noether Currents Time Translation and Energy...

Table of Contents Introduction Historical Context Symmetry in Physics Global vs Local Symmetries Gauge Symmetry: Core Idea Electromagnetism as a Gauge Theory Gauge Fields and Covariant Derivative U(1) Gauge Symmetry and Quantum...

Table of Contents Introduction Motivation and Scope of Perturbation Theory Basics of Perturbative Expansion Role in Quantum Field Theory Feynman Diagrams and Expansion in Coupling Constant Orders in Perturbation Theory Tree-Level...

Table of Contents Introduction Historical Background and Motivation Why Use Feynman Diagrams? Perturbation Theory in QFT Building Blocks of Feynman Diagrams Feynman Rules Overview External Lines and Particle States Propagators Vertices and Coupling...

Table of Contents Introduction Historical Background and Development Classical Electrodynamics Recap The Need for a Quantum Theory of Electromagnetism QED as a Quantum Field Theory The QED Lagrangian Gauge Symmetry and...

Table of Contents Introduction First Quantization Recap What is Second Quantization? Motivation and Physical Meaning Fock Space and Quantum States Creation and Annihilation Operators Commutation and Anticommutation Relations Field Operators Operator Algebra Example: Quantization...

Table of Contents Introduction What Are Spinors? Motivation from Lorentz Group Representations Spinor Transformation Properties Types of Spinors Dirac Spinors and 4-Component Representation Gamma Matrices and Clifford Algebra Representations of Gamma Matrices Dirac...

Table of Contents Introduction Motivation and Historical Context The Need for a Relativistic Wave Equation Inadequacy of the Klein-Gordon Equation Dirac’s Insight: First-Order Equation Mathematical Form of the Dirac Equation Gamma...

Table of Contents Introduction What is Quantization? Classical vs Quantum Descriptions Canonical Quantization: Overview From Classical Mechanics to Field Theory Canonical Variables and Poisson Brackets Field Commutation Relations Scalar Field Quantization Mode Expansion...

Table of Contents Introduction Historical Background Relativistic Foundations Derivation of the Klein-Gordon Equation Lagrangian Formulation Euler-Lagrange Equation for Fields Plane Wave Solutions Canonical Quantization Creation and Annihilation Operators Commutation Relations Energy-Momentum Tensor Feynman Propagator Complex Klein-Gordon Field Symmetries...

Table of Contents Introduction Motivation and Overview Fields as Physical Quantities Types of Classical Fields Lagrangian Formulation of Field Theory Euler-Lagrange Equations for Fields Example: Scalar Field Electromagnetic Field as a Classical...