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Contents

• V Full version
• 0 Introduction
• 1 Classical field theory
• 1.1 Classical fields
• 1.2 Lorentz invariance
• 1.3 Symmetries and Noether's theorem for field theories
• 1.4 Hamiltonian mechanics
• 2 Free field theory
• 2.1 Review of simple harmonic oscillator
• 2.2 The quantum field
• 2.3 Real scalar fields
• 2.4 Complex scalar fields
• 2.5 The Heisenberg picture
• 2.6 Propagators
• 3 Interacting fields
• 3.1 Interaction Lagrangians
• 3.2 Interaction picture
• 3.3 Wick's theorem
• 3.4 Feynman diagrams
• 3.5 Amplitudes
• 3.6 Correlation functions and vacuum bubbles
• 4 Spinors
• 4.1 The Lorentz group and the Lorentz algebra
• 4.2 The Clifford algebra and the spin representation
• 4.3 Properties of the spin representation
• 4.4 The Dirac equation
• 4.5 Chiral/Weyl spinors and γ⁵
• 4.6 Parity operator
• 4.7 Solutions to Dirac's equation
• 4.8 Symmetries and currents
• 5 Quantizing the Dirac field
• 5.1 Fermion quantization
• 5.2 Yukawa theory
• 5.3 Feynman rules
• 6 Quantum electrodynamics
• 6.1 Classical electrodynamics
• 6.2 Quantization of the electromagnetic field
• 6.3 Coupling to matter in classical field theory
• 6.4 Quantization of interactions
• 6.5 Computations and diagrams