Established physics · Lesson 17 of 34
Read the marks in a Feynman diagram
A Feynman diagram is a calculation map: its lines name field contributions and its vertices name allowed interactions.
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A visual key for fields, vertices, and arrows
Start with the question, not the squiggles
A diagram answers: given these prepared incoming particles, which outgoing particles can this quantum process produce, and with what quantum amplitude? It is one term in a calculation, not a camera view of little objects taking the drawn paths. The same process may have several diagrams whose amplitudes must be combined.
Straight lines: matter
A solid line with an arrow conventionally stands for a fermion contribution: an electron, neutrino, muon, or quark, for example. Read the written label to identify the species. The arrow marks fermion flow and helps distinguish particle from antiparticle; it is not automatically the direction of travel, and diagrams do not all draw time in the same direction.
Wavy, curly, and dashed
Wavy lines commonly stand for a photon, W, or Z; the label decides which. Curly lines commonly represent gluons. Dashed lines commonly represent a scalar such as the Higgs. Styles can vary by author, especially in more advanced theories, so the label and diagram key outrank the look of a line.
A vertex is a permitted connection
At a vertex, field lines meet according to a coupling in the theory. An electron can meet a photon line; a muon and its neutrino can meet a W line. You cannot freely join any three names. A permitted vertex also does not guarantee that a complete reaction has enough energy or obeys every conservation law.
Outside ends and inside lines
An external line meets the edge of a diagram and represents a prepared incoming or specified outgoing particle state. An internal line connects vertices inside the calculation. The internal W in muon decay is called virtual: it is a contribution in the amplitude, not a separately detected, freely propagating W boson.
Loops and more than one route
A closed line path is a loop: an additional quantum contribution. A simple tree diagram can be the leading term, while diagrams with loops alter the prediction. Amplitudes for indistinguishable permitted routes combine before a probability is found. One drawing by itself is seldom the whole prediction.
Where the method stops being simple
These pictures are especially useful when a few diagram terms give a good approximation. In strongly coupled situations such as quark confinement, a small set of diagrams cannot simply give the whole answer; other tools, including lattice calculations, are important. The underlying field rules still apply.
The layout is calculation bookkeeping. The marks do not map the exact positions or trajectories of particles.
Takeaway: Read labels → line kinds → allowed vertices → incoming/outgoing states. Then remember that diagrams contribute amplitudes, not photographs.
Check your understanding
What does a solid arrowed line usually indicate?
- A fermion contribution, such as a quark or lepton
- Always a photon
- The direction that time must flow
Answer and explanation
A fermion contribution, such as a quark or lepton
Solid arrowed lines usually denote fermions; the label identifies which one.
A wavy line is marked W⁻. What is it?
- A gluon
- A weak W contribution
- Necessarily a photon
Answer and explanation
A weak W contribution
The W⁻ label identifies it; line style alone is not enough.
What does a meeting point of lines mean?
- Fields interact through an allowed coupling
- A photographed collision location
- Any fields may connect there
Answer and explanation
Fields interact through an allowed coupling
A vertex represents a coupling permitted by the theory.
Which line represents a specified incoming or outgoing particle?
- An external line
- Any internal line
- Only a loop
Answer and explanation
An external line
External line ends represent the prepared or specified states.
Why can an antiparticle arrow point opposite to its outgoing motion?
- Arrows indicate fermion flow, not always motion
- Antiparticles truly move backward in clock time
- The diagram is broken
Answer and explanation
Arrows indicate fermion flow, not always motion
Arrow convention distinguishes fermion and antifermion flow.
What does a closed loop add?
- A quantum contribution to the amplitude
- A literal tiny orbit observed by a camera
- An extra fundamental force
Answer and explanation
A quantum contribution to the amplitude
Loop diagrams encode additional contributions in a perturbative calculation.
Use the interactive trainer for demonstrations, the field explorer, and saved checkpoint progress.