People who learn physics without a university course usually ask me the same thing first: what should I read, and in which order? My answer is classical mechanics, then electrodynamics, then quantum mechanics, then quantum field theory. That is also the order of a typical physics degree, but the reason is not tradition. Each subject reuses specific tools from the ones before it, and when I wrote one book for each of the four, I could see exactly where.
This post shows those dependencies concretely, with page numbers from my four books, so you can see what you would be missing if you skipped a step. It ends with the mathematics each step needs.
The concept map
The table lists 13 concepts and the page where each one is developed in No-Nonsense Classical Mechanics (CM), Electrodynamics (ED), Quantum Mechanics (QM) and Quantum Field Theory (QFT). A dash means the book does not develop it. Read across a row and you see the same idea being reused, usually in a more general form.
| Concept | CM | ED | QM | QFT |
|---|---|---|---|---|
| Action and least action | p73 | - | p204 (path integral) | p137 |
| Euler-Lagrange equation | p86 | - | - | p141, for fields p153 |
| Hamiltonian and time evolution | p93 | - | p75 (Schrödinger equation) | p285 |
| Poisson bracket to commutator | p107 | - | p73 | p307 (field commutators) |
| Noether's theorem | p223 | - | - | p155 |
| Harmonic oscillator | p181 | - | p141 | p294 |
| Phase space | p49 | - | p219 | - |
| Fields and wave equations | - | p42, p82 | - | p69, p112 |
| Special relativity | p297 | p163 | - | p37 |
| Gauge symmetry | - | p175 | - | p129, p264 |
| Spin and spinors | - | - | p85 | p94, Dirac equation p195 |
| Path integral | - | - | p204 | p535 |
| Delta distribution and Green's functions | - | p301 | p257 | p236 |
Pages from the current paperback editions, read from each book's table of contents and index.
Two things stand out. First, QFT appears in almost every row: it is the subject that combines all the others. Second, classical mechanics feeds more rows than electrodynamics does. That is why I would never skip mechanics, while a reader who only wants quantum mechanics can, if necessary, postpone electrodynamics.
Step 1: classical mechanics
Most of what comes later is written in the language of classical mechanics. The Lagrangian you meet here is the same kind of object every quantum field theory is built from; in my QFT book the Euler-Lagrange equation for fields (p153) is the direct generalization of the one in the mechanics book (p86). The Hamiltonian becomes the energy operator in the Schrödinger equation. The Poisson bracket {x, p} = 1 becomes the commutator [x, p] = iħ. The harmonic oscillator appears in all three later books, and in QFT a free field is literally a collection of harmonic oscillators.
What to learn: Newton's laws, the Lagrangian and Hamiltonian formulations and how they connect, Noether's theorem, the harmonic oscillator.
Math you need: calculus in several variables and partial derivatives. The Legendre transform and Lagrange multipliers can be learned on the way.
Guide: classical mechanics for self-study.
Step 2: electrodynamics
Electrodynamics is the first field theory most people learn. The electric and magnetic fields live everywhere in space, and Maxwell's equations describe how they change. Two ideas from here matter a lot later.
The first is special relativity. It came out of electrodynamics: Maxwell's equations predict a speed for electromagnetic waves that does not depend on the observer, and taking that seriously gives special relativity. QFT starts with a 32-page chapter on spacetime (p37 to p68) because it cannot work without it.
The second is gauge freedom. The electromagnetic potential can be changed without changing the fields. In electrodynamics this looks like a technicality. In quantum field theory it becomes the principle from which all known interactions follow: the QFT book introduces gauge fields on p129 and gauge interactions on p264, and both build on what electrodynamics already showed.
What to learn: Maxwell's equations, potentials and gauge transformations, electromagnetic waves, the relativistic form of the equations.
Math you need: vector calculus (divergence, curl, Gauss's and Stokes' theorems). This is the real hurdle; my electrodynamics book has a 70-page appendix on it.
Guide: electrodynamics for self-study.
Step 3: quantum mechanics
With the Hamiltonian formalism from mechanics in hand, the canonical commutation relation looks like a modification of something familiar, not a rule from nowhere. The harmonic oscillator, solved with creation and annihilation operators (QM p141), is the model you will reuse for free quantum fields (QFT p294 and p309).
The part of quantum mechanics that QFT relies on most is not the part most first courses emphasise. Many first courses spend most of their time on wave functions and solving the Schrödinger equation for specific potentials. QFT needs operators, commutators, the Heisenberg picture and the path integral. That is why my QM book has a whole part on the formulations beyond wave functions (p187 to p232).
What to learn: states and observables, the Schrödinger equation, the harmonic oscillator and the hydrogen atom, spin, perturbation theory, and the alternative formulations.
Math you need: linear algebra (eigenvalues, Hermitian matrices), complex numbers, the Fourier transform.
Guide: quantum mechanics for self-study.
Step 4: quantum field theory
Quantum field theory combines the previous three: fields and gauge symmetry from electrodynamics, quantization from quantum mechanics, and the Lagrangian formalism from classical mechanics. When one of them is shaky, a QFT book feels impossible, which is the main reason people give up on it.
When I wrote my QFT book I made that explicit. Its first quantum field appears on page 301 of 642. The 236 pages before Part I (p37 to p272) build spacetime, classical fields, the Lagrangian formalism and classical interactions, because those are the places where QFT readers usually get stuck.
What to learn: free scalar, Dirac and gauge fields, canonical quantization, Feynman diagrams and scattering amplitudes, renormalization, symmetry breaking.
Math you need: everything above, plus the index notation of special relativity.
Guide: quantum field theory for self-study.
Can I change the order?
- Quantum mechanics before electrodynamics: possible. The table shows few direct dependencies between ED and QM. You will meet electrodynamics again in the hydrogen atom and in spin, but you can follow those without a full course.
- Quantum mechanics before classical mechanics: possible, but you lose the Hamiltonian, the Poisson bracket and the harmonic oscillator as familiar starting points, and quantum mechanics looks more arbitrary.
- QFT before electrodynamics: I would not. Special relativity and gauge symmetry are both needed from the first chapters.
Books for each step
I wrote one book for each step: No-Nonsense Classical Mechanics, No-Nonsense Electrodynamics, No-Nonsense Quantum Mechanics and No-Nonsense Quantum Field Theory. They use one notation throughout, and each ends with recommendations for reading further. They have no exercise sets, so each guide above names a problem book to pair them with. If you want to compare them with the standard textbooks first, see the rankings for classical mechanics, electrodynamics, quantum mechanics and quantum field theory.
Jakob Schwichtenberg