Preface
Acknowledgements
Author biography
Units and conventions
1 Classical field theory
1.1 Lagrangian formalism for fields
1.2 The Klein-Gordon field
1.3 The electromagnetic field
1.4 Lorentz invariance
1.4.1 Rotations
1.4.2 Boosts
1.4.3 An example of a Lorentz-invariant quantity
1.5 Transformation of fields under Lorentz transformations
1.6 Noether's theorem
1.6.1 Implications of Noether's theorem
1.7 Applications of Noether's theorem
1.7.1 Translational invariance
1.7.2 The Klein-Gordon energy-momentum tensor
1.7.3 Angular momentum and Lorentz transformations
1.8 The Hamiltonian formalism for fields
1.8.1 Hamilton's equations for fields
References
2 Quantization of free fields
2.1 The quantum linear chain and phonons
2.1.1 Going from classical to quantum
2.1.2 Construction of the vacuum and many phonon states
2.2 Poisson brackets in classical field theory
2.3 Quantization of a free scalar field theory
2.3.1 Quantized Hamiltonian operator
2.3.2 Vacuum renormalization and normal ordering
2.3.3 A note on dimensions
2.3.4 The vacuum state
2.3.5 Single particle states
2.4 Multi-particle states and Fock space
2.5 Complex scalar fields
2.6 Quantization of a complex scalar field
2.7 Causality
2.8 Propagators
2.9 Propagators as Green's functions
References
3 Quantization of interacting field theories
3.1 Weakly-interacting scalar fields
3.2 Two examples of interacting quantum field theories
3.3 The interaction picture and Dyson's equation
3.3.1 Dyson's formula
3.4 Interactions in scalar Yukawa theory
3.5 The S-matrix
3.5.1 Example: pion decay in the scalar Yukawa model
3.6 Beyond leading-order perturbation theory
3.6.1 Wick's theorem
