Unit 3098: Introduction to Quantum Field Theory

1. Introduction to Quantum Field Theory

• Overview of QFT and its significance in modern physics
• Basic concepts: fields as fundamental entities
• Quantization of fields: motivation and approach
• Creation and annihilation operators: definitions and roles
• Vacuum fluctuations and their physical interpretations

2. Classical Field Theory

• Classical fields as precursors to quantum fields
• The Lagrangian formalism for fields
  • Action principle
  • Lagrangian density
• Euler-Lagrange equations for fields
• Classical field equations
  • Maxwell's equations as a case study
• Energy-momentum tensor and conservation laws

3. Quantization of Fields

• Transition from classical to quantum fields
• Canonical quantization procedure
  • Commutation and anticommutation relations
• Quantization of different types of fields:
  • Scalar fields
  • Spinor fields (Dirac fields)
  • Vector fields (e.g., electromagnetic field)

4. Feynman Diagrams

• Introduction to Feynman diagrams as a computational and conceptual tool
• Rules for constructing Feynman diagrams
  • External and internal lines
  • Vertices and interaction points
• Interpretation of diagrams in perturbation theory
• Examples of simple interaction processes

5. Renormalization

• Divergences in QFT calculations and their origin
• Regularization techniques
  • Cutoff methods
  • Dimensional regularization
• Renormalization procedure
• Renormalization group flow and its physical meaning

6. Symmetries in Quantum Field Theory

• Role of symmetries in physics
• Global vs local symmetries
• Noether's theorem
  • Connection between symmetries and conservation laws
• Gauge symmetries and gauge fields

7. Standard Model of Particle Physics

• Overview of the Standard Model as a QFT
• Particle content:
  • Leptons, quarks, gauge bosons, and the Higgs boson
• Gauge symmetries:
  • SU(3) × SU(2) × U(1) groups
• The Higgs mechanism and spontaneous symmetry breaking

8. Quantum Field Theory in Curved Spacetime

• Motivation for extending QFT to curved spacetime
• Effects of gravity on quantum fields
• Concept of particle creation in expanding universes
• Hawking radiation from black holes
• Implications for cosmology and black hole physics