Instructor: Hong, Theoretical Physicist specializing in various topics like quantum gravity and statistical physics.
Objective: Develop concepts for quantum dynamics of fields. Understand classical and quantum distinctions through examples like Maxwell’s equations.
Goals of the Course
Quantum Electrodynamics: Transition from classical understanding to quantum mechanics of electric and magnetic fields leading to the concept of photons.
Quantum Field Theory (QFT): Fundamental theory for three of the four fundamental interactions; also extends to partial applications in quantum gravity.
Importance in Other Fields: QFT is a universal language in theoretical physics, applicable in various branches such as condensed matter physics and statistical physics.
Structure: This course will lay foundational concepts. Subsequent courses (QFT 2 and 3) will focus more on technical development.
Topics: List provided in the outline, but subject to change based on course pace.
Misconceptions and Learning Approach
Perceived Difficulty: Instructor emphasizes QFT can be manageable if learned correctly, likening it to quantum mechanics in terms of conceptual challenges.
Calculation-Heavy Nature: Amount of calculations is a fact but not the main difficulty; focus is on conceptual understanding.
Developing Intuition: Importance of examples and exercises to build intuition like in quantum mechanics.
Study Outside Class: Lecture highlights concepts; in-depth learning and problem-solving occurs through self-study and problem sets.
Notation Differences: Acknowledges different notations used in recommended textbooks (Peskin and Weinberg) and lectures.
Basic Concepts in Quantum Field Theory
Classical Field Theory (CFT) to QFT
Principle of Locality: Physical processes involve local interactions across space without action at a distance.
Example: Maxwell equations locally relate electric and magnetic fields.
Application: Also in Einstein's general relativity (local equations for space-time metric).
Functional Forms in Lagrangian Mechanics
Classical Mechanics Recap: Introduction to Lagrangian and Hamiltonian mechanics for classical systems.
Generalization to Field Theory: Extending principles to systems with infinite degrees of freedom.
Canonical Momentum and Hamiltonian Density:
Canonical momentum density as: π^a (x) = ∂L/∂(∂_µφ^a)
Hamiltonian density:
H = π^a ∂_0φ^a - L
Equation of Motion: Derived by extremizing the action, relating fields and their dynamics.
Principles and Examples
Translation and Lorentz Invariance: Ensuring physical laws are the same across different locations and frames of reference.
Examples:
Maxwell's Theory: Describing electromagnetism.
Einstein Gravity: Introducing the general relativity field equations.
Scalar Field Theory: Simplest field theory; includes examples like the Higgs field and pions.
Practical Guidance
Notation and Conventions: Clarification on use of indices and shorthand notations throughout derivations.
Worked Examples and Intuition-Building: Emphasis on solving problems and understanding underlying physics through practice.
Homework: Important in grasping real-world applications and advancing past conceptual hurdles.
Challenges: Keeping in mind complexity often comes from conceptual rather than computational aspects.