3.2.1.4ParticlesStretch

Particle Interactions and Feynman Diagrams

Two electrons never touch, and yet they repel each other. So how does one particle "know" another is nearby? The particle-physics answer is that every force is really a rapid exchange of $virtual particles$ passed between the interacting bodies. $Feynman diagrams$ give a compact, exact way to draw these exchanges — and to check, at a glance, whether a proposed interaction is even allowed.

40 min Video by Physics Online 3.2.1 Particles

Feynman Diagrams — A Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Name the four fundamental interactions and their associated exchange particle
Explain how the range of a force relates to the mass of its exchange particle
Read and draw simple Feynman diagrams for electromagnetic, weak and strong interactions
Apply conservation of charge at every vertex of a Feynman diagram
Interpret a beta-decay Feynman diagram in terms of the W boson

Four forces, four exchange particles

All particle interactions are explained by just four fundamental forces, and each is modelled as an exchange of a specific $gauge boson$ between the interacting particles. The $electromagnetic force$ (acts between charged particles) is carried by the $virtual photon$ ; the $strong force$ (binds quarks and nucleons) by the $gluon$ ; the $weak force$ (responsible for beta decay and other particle transformations) by the $W⁺, W⁻ and Z⁰ bosons$ ; and gravity, not really examined at this level, by the hypothetical graviton.

The range of a force is controlled by the mass of its exchange particle: a massive exchange particle can only exist as a virtual particle for a very short time (by the energy–time uncertainty principle), so it can only travel a short distance before it must be reabsorbed — giving a short-range force. The photon and gluon are (effectively) massless, but while the photon gives electromagnetism an infinite range, the gluon’s force is confined to within the nucleus by the strong force’s own self-interaction. The W and Z bosons are extremely massive (about 80–91 times the proton’s mass), which is exactly why the weak interaction has such a tiny range — a thousand times smaller than a proton.

Tip — Heavy exchange particle → short-range force. The weak force’s W/Z bosons are the heaviest of the lot, which is why the weak interaction has by far the shortest range.

Reading a Feynman diagram

A Feynman diagram plots space horizontally and time running $up the page$ . Straight lines represent matter particles (fermions — quarks and leptons); an arrow pointing forward in time represents a particle, while an arrow pointing backward in time represents its antiparticle. Wavy or dashed lines represent the exchange (gauge) boson, connecting two straight lines at a $vertex$ — the point where the interaction actually happens.

Every vertex must independently conserve charge (and, as you’ll see in a later lesson, baryon number and lepton number too). This is the single most useful exam skill here: given an incomplete diagram, you can identify the missing particle just by making the charge balance at its vertex.

Tip — At a vertex, add up the charges of the particles going in and check they equal the charges of the particles coming out — the exchange particle itself carries charge too if it is a W⁺ or W⁻.

Electromagnetic repulsion between electrons

Two electrons approaching each other exchange a single virtual photon. On the diagram: an electron line enters from the bottom left, a second electron line enters from the bottom right, a wavy photon line joins the two straight lines between them, and the two electron lines then continue upward and outward, having been deflected. Charge is conserved at each vertex because the electron’s charge is unchanged before and after emitting or absorbing an (uncharged) photon.

This is the general picture for $any$ electromagnetic interaction between charged particles — the repulsion (or attraction) is the macroscopic result of a huge number of virtual photon exchanges.

Beta-minus decay as a Feynman diagram

Beta-minus decay ( $n \to p + e^{-} + \overset{ν}{ˉ}_{e}$ ) is drawn as a single neutron line entering from below, changing into a proton line at a vertex, with a $virtual W⁻ boson$ emitted from that vertex. The W⁻ boson then decays at a second vertex into an electron and an antineutrino, which leave the diagram as two separate outgoing lines.

Checking charge: the neutron (0) becomes a proton (+1) plus a W⁻ (−1) at the first vertex — $0 = (+ 1) + (- 1)$ , balanced. At the second vertex the W⁻ (−1) becomes an electron (−1) and an antineutrino (0) — again balanced. This is exactly why the weak interaction, and only the weak interaction, can change a quark’s flavour (turn a down quark into an up quark, and hence a neutron into a proton) — no other force carries the charge needed to do it while also converting the type of particle.

Tip — Whenever a decay converts one type of particle into a genuinely different type (n → p, or one quark flavour into another), it has to be the weak interaction — the electromagnetic and strong forces can change a particle’s motion but never its identity.

Common mistakes to avoid

Thinking Feynman diagrams show real particle paths in space.

A Feynman diagram is a bookkeeping tool for an interaction — the axes represent space and time schematically, not an actual trajectory.

Assuming every force has the same range because "forces are forces".

Range depends on the exchange particle’s mass — massless photons give electromagnetism infinite range, but the very massive W/Z bosons confine the weak force to within the nucleus.

Forgetting that the exchange particle itself can carry charge.

A W⁺ or W⁻ boson carries charge, so you must include it when checking that charge balances at each vertex — only the photon, Z⁰ and gluon are uncharged.

Key takeaways

The four fundamental forces are electromagnetic (photon), strong (gluon), weak (W⁺, W⁻, Z⁰) and gravity (graviton, not examined in detail).
A more massive exchange particle means a shorter-range force — the heavy W/Z bosons give the weak force its extremely short range.
On a Feynman diagram, time runs up the page; forward-time arrows are particles, backward-time arrows are antiparticles, and boson lines join vertices.
Charge (and baryon/lepton number) must be conserved at every single vertex — this lets you deduce a missing particle on an incomplete diagram.

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Particle Interactions and Feynman Diagrams

Two electrons never touch, and yet they repel each other. So how does one particle "know" another is nearby? The particle-physics answer is that every force is really a rapid exchange of

virtual particles

passed between the interacting bodies.

Feynman diagrams

give a compact, exact way to draw these exchanges — and to check, at a glance, whether a proposed interaction is even allowed.

40 min Video by Physics Online 3.2.1 Particles