Here are some notes I made while reading Coleman's QFT book. For the most part, the book is quite clear in its derivations and explanations, so these notes
are mainly reminders for me, along with filling in a few points glossed over in the book. Hopefully the notes may be of use to others.**Note
that these notes are designed to be used for someone reading through Coleman's book, so I won't include derivations that are explicitly
done in the book.**

The book does have a number of problems to work on, but complete, detailed solutions to the problems are included in the book, so I don't see much point in reproducing those here.

For anyone seriously interested in learning quantum field theory, I would recommend Coleman's book above every other book I've looked at. Perhaps due to its size (more than 1100 full-sized pages), it has more space than other books to explain things thoroughly, although I think a lot of the reason is Coleman's exceptionally clear teaching style. The book is essentially a transcription of his lecture notes given in the Physics 253 course at Harvard.

**Chapter 1 - Special relativity and quantum mechanics**

- Section 1.2 - A free spinless particle
- Translation and rotation invariance
- Relativistic invariant integration measure
- Lorentz transformations of relativistic states
- Section 1.3 - Determination of the position operator X

**Chapter 2 - The simplest many-particle theory**

- Sections 2.1, 2.2 - Fock space and occupation number
- We've covered these in a previous post: Fock space & the number operator
- Section 2.3 - Operator formalism and the harmonic oscillator
- Also covered earlier: Harmonic oscillator: algebraic solution
- Harmonic oscillator: algebraic normalizaton of raising and lowering operators
- Section 2.4 - Operator formalism and Fock space

**Chapter 3 - Constructing a scalar quantum field**

- Sections 3.1, 3.2, 3.3

**Chapter 4 - The missing box**

- Section 4.1
- Section 4.3
- Sections 4.4 & 4.5

**Chapter 5 - Symmetries and conservation laws I. Spacetime symmetries**

- Section 5.1
- Sections 5.3, 5.4
- Section 5.5
- Section 5.6

**Chapter 6 - Symmetries and conservation laws II. Internal symmetries**

- Section 6.1
- Section 6.3