By Jakob Schwichtenberg, author of No-Nonsense Quantum Field Theory (642 pages). Page numbers refer to the current paperback; counts come from the LaTeX source.
Quantum field theory is the subject where self-study most often fails, and in my view the reason is rarely QFT itself. A QFT book uses special relativity, classical field theory, the Lagrangian formalism and quantum mechanics at the same time, and the standard texts assume all four. If one is weak, the book becomes unreadable from the first chapter. No-Nonsense Quantum Field Theory is built around that problem: the first quantum field appears on page 301, almost halfway through, after a long preliminary part that builds everything QFT needs.
Where to start depends on what you know
Because of that structure, not everyone should start on page 1. Use this table:
| You are comfortable with | Start at | Pages you can skim |
|---|---|---|
| Quantum mechanics only | Chapter 1 (p23), then Part 0 from p37 | none |
| Quantum mechanics and special relativity with four-vectors | Chapter 3, Fields (p69) | Chapter 2, Spacetime (p37 to p68) |
| Also the Lagrangian formalism for fields and the Klein-Gordon and Dirac equations | Chapter 6, Interacting Classical Fields (p235) | Chapters 2 to 5 (p37 to p234) |
| All of the above, including classical gauge interactions | Part I, Chapter 7 (p273) | Part 0 (p37 to p272) |
Part 0 is 236 pages, 37% of the book. Skim it even if you skip it: the notation and conventions used later are set there.
The book in numbers
- 1,089 calculation steps annotated in the margin, more than the other three No-Nonsense books together.
- 1,826 sidenotes.
- 243 figures.
- Two appendices of "cumbersome calculations" (p589 to p618) that work out in full the steps a course text leaves as exercises, such as the a(k), a†(k) commutation relations (p595), the proof that the Feynman propagator is a Green's function (p601) and Wick's theorem for three fields (p611).
Stage 1: the preliminaries (Part 0, pages 37 to 272)
Chapter 2 (p37) covers spacetime: maximum speed, time dilation, proper time, the Minkowski metric and four-vectors (p51), the energy-momentum relation (p57) and Lorentz and Poincaré transformations (p62). Chapter 3 (p69) introduces the fields: scalar (p72), vector (p74), spinor (p94) and gauge fields (p129). Chapter 4 (p137) is the Lagrangian formalism, with the Euler-Lagrange equation (p141), its field-theory version (p153) and Noether's theorem (p155). Chapter 5 (p167) derives the free field equations: Klein-Gordon (p170), Dirac (p195) and Proca/Maxwell (p214). Chapter 6 (p235) adds interactions, still classically: Green's functions (p236), self-interactions (p246), Yukawa (p253) and gauge interactions (p264).
- Write the Klein-Gordon Lagrangian and derive the Klein-Gordon equation from it.
- What is a spinor, and why does it change sign under a full rotation?
- Derive the conserved current of a complex scalar field from Noether's theorem.
- What is a Green's function, and why do we need it for interacting fields?
Stage 2: quantum fields (Part I, pages 273 to 406)
Chapter 7 (p273) is a compact review of quantum mechanics, focused on what QFT needs, including the harmonic oscillator (p294). Chapter 8 (p301) quantizes fields: how they differ from classical fields (p304), the canonical commutation relations (p307), field operators (p309), particle states (p322), propagators (p334), and complex scalar (p351), spinor (p358) and gauge fields (p367). Chapter 9 (p379) sets up interactions: transition amplitudes, the interaction picture (p382), the Dyson series (p384) and the ground state energy (p394).
- Why does the canonical commutation relation for a field imply that its excitations behave like particles?
- What does the Feynman propagator describe physically?
- Why do we switch to the interaction picture for interacting fields?
Stage 3: calculating amplitudes (Part II, pages 407 to 512)
Chapter 10 (p407) does a first scattering calculation by brute force. Chapter 11 (p421) builds the tools that make it manageable: contractions (p423), Wick's theorem (p428), important contractions (p430), Feynman diagrams (p441), and scattering done the efficient way (p448). Chapter 12 (p465) applies them to Yukawa (p467) and gauge interactions (p481). Chapter 13 (p487) covers virtual particles (p488), loops (p491), regularization (p493) and the renormalization group (p498).
This is where to start working problems. My book has worked calculations but no exercise sets. Schwartz's Quantum Field Theory and the Standard Model and Peskin and Schroeder both have extensive problems at the end of their chapters; work the problems from their chapters on the same topic as you finish each chapter here.
- State Wick's theorem and use it to reduce a product of four field operators.
- Draw the tree-level Feynman diagram for 2 → 2 scattering in φ⁴ theory and write the amplitude.
- What is a running coupling, and why does it follow from renormalization?
Stage 4: the deeper structure (Part III, pages 513 to 588)
Chapter 14 (p513) is about the vacuum: explicit and spontaneous symmetry breaking (p519 and p521) and spontaneous mass generation (p529), the mechanism behind the Higgs. Chapter 15 (p535) introduces the path integral, first in quantum mechanics (p536) and then in QFT (p549). Chapter 16 (p553) covers non-perturbative phenomena such as instantons (p556). Chapter 17 (p565) explains effective field models and why fundamental Lagrangians are so simple.
What to read next
The reading list at the end of the book sorts the options like this:
- Same spirit, for a second opinion: Klauber, Student Friendly Quantum Field Theory, and Lancaster and Blundell, Quantum Field Theory for the Gifted Amateur (Oxford, $56).
- More advanced but readable: Schwartz, Quantum Field Theory and the Standard Model (Cambridge, $104), and Srednicki, Quantum Field Theory.
- Free lecture notes: David Tong's QFT notes and Sidney Coleman's lectures.
- Standard but far less student-friendly: Peskin and Schroeder (calculation-focused) and Weinberg's The Quantum Theory of Fields (focused on why). See Peskin and Schroeder compared.
- Path integral: Zee, Quantum Field Theory in a Nutshell, best once you already understand QFT, and Ryder, Quantum Field Theory.
All of them are compared on best quantum field theory books for beginners.
Common questions
Can I learn QFT without a physics degree?
Yes, if you build the foundations. The guides for classical mechanics, electrodynamics and quantum mechanics cover what to read first. Part 0 of the book then fills the gaps in special relativity and classical field theory.
Should I start with the path integral or canonical quantization?
Both lead to the same Feynman rules. Canonical quantization builds directly on quantum mechanics, so the book uses it first and introduces the path integral in Chapter 15.
Why is the book 642 pages if it is "no-nonsense"?
Because it skips no steps. The 236 pages of preliminaries and the two appendices of full calculations are the material other books assume or leave to the reader.