Here are some notes on the book W. Greiner & J. Reinhardt, Field Quantization, Springer-Verlag (1996). The book contains no exercises for the reader (well, there are exercises, but the solutions are given in detail in the book), so I'm providing only my own notes on the text in an effort to clarify some points that I found a bit confusing.

**Chapter 1: Classical and Quantum Mechanics of Particle Systems**

- 1.4 Linear chain of oscillators - Classical treatment, equations of motion
- 1.4, Ex. 1.1 Linear chain of oscillators - Classical treatment, Hamiltonian
- 1.5 Linear chain of oscillators - Quantum treatment
- 1.5, Ex. 1.2 Linear chain of oscillators - External force, unitary operator
- 1.5, Ex. 1.2 Linear chain of oscillators - External force, ground state

**Chapter 2: Classical Field Theory**

- 2.1, 2.3 Functional derivatives and the Lagrangian
- 2.2 Hamilton’s equations of motion in classical field theory
- 2.2 Poisson brackets and Hamilton’s equations of motion
- 2.4 Coordinate transformations in classical field theory
- 2.4 Noether’s theorem and conservation laws
- 2.4 Noether’s theorem and conservation of energy and momentum
- 2.4 Lorentz transformations as rotations
- 2.4 Lorentz transformations as 2×2 matrices
- 2.4 Lorentz transformations and the special linear group SL(2,C)
- 2.4 Lorentz transformation as product of a pure boost and pure rotation
- 2.4 Noether’s theorem and conservation of angular momentum

**Chapter 3: Nonrelativistic quantum field theory**

- 3.1 Lagrangian for the Schrödinger equation
- 3.2 Nonrelativistic field theory - Schrödinger equation
- 3.2 Nonrelativistic field theory - Fourier expansion
- 3.2, Ex 3.1 Nonrelativistic field theory - number, creation and annihilation operators
- 3.2 Nonrelativistic field theory - Fock space to position space
- 3.3 Nonrelativistic field theory for fermions

**Chapter 4: Spin-0 Fields: The Klein-Gordon Equation**