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 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**