Quantum Field Theory I

Summary of the course PHYS-F410

The notes published on this website are based on my personal understanding of the material and have not been independently verified. While I hope they are helpful, there may be errors or inaccuracies. If you find any errors or have suggestions for improvement, please feel free to contact me: a.d@csic.es.

Teacher: Petr TINIAKOV (Year 2023-2024)
Official resources: ULB page Dochub space

Table of Contents

Chapter 1: Classical Field

  • 1.1 Scalar field
  • 1.2 Symmetries and conservation laws: Noether theorem
  • 1.3 Energy-momentum tensor

Chapter 1 Notes

Chapter 2: Quantization of a Free Scalar Field

  • 2.1 Quantization in quantum mechanics
  • 2.2 Quantization of a real scalar field
  • 2.3 Complex scalar field

Chapter 2 Notes

Chapter 3: Interaction

  • 3.1 Interaction representation
  • 3.2 Evolution in interaction representation
  • 3.3 Matrix Elements of the S-Matrix
  • 3.4 Calculation of the S-Matrix
  • 3.5 Decay of a massive particle
  • 3.6 Scattering and Cross section

Chapter 3 Notes

Chapter 4: Free Dirac Field

  • 4.1 Spinor representation
  • 4.2 Lagrangian of a free Dirac field
  • 4.3 Solution to the free Dirac equation
  • 4.4 Quantization
  • 4.5 Spin
  • 4.6 One-particle states
  • 4.7 Statistics

Chapter 4 Notes

Chapter 5: Vector Field

  • 5.1 Construct a Lagrangian
  • 5.2 Classical solutions
  • 5.3 Canonical quantization

Chapter 5 Notes

Chapter 6: Feynman Rules for Fermions and Vectors

  • 6.1 Feynman rules for fermions
  • 6.2 Feynman rules for vectors
  • 6.3 Decay of a vector into two fermions

Chapter 6 Notes