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Established physics · Lesson 24 of 34

Use the 25-field atlas as a prediction map

A field card lets you check possible interactions; a full calculation still needs dynamics and data.

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401 · integrate properties, vertices, and limits

Step one: name the states

Write down the incoming and outgoing excitations, their charges, and whether they carry color. For μ⁻ decay, the outgoing e⁻, νμ, and anti-νe belong to different field descriptions. The muon does not merely change its vibration within one common lepton field.

Step two: propose connections

Ask which vertices the couplings permit: a W-mediated charged-current connection for muon decay, a photon for direct electromagnetic scattering, a gluon for direct color scattering. Each vertex must obey the appropriate conservation rules.

Step three: check energy and rate

Even an allowed vertex may be unavailable to on-shell final states at a given energy. Coupling strength and phase space affect rates, and different diagrams can interfere. A Feynman diagram is one contribution to an amplitude, not a promise that every allowed event happens.

The electron as a stringent target

A complete mathematical account of the electron needs the right spin, electric charge, color singlet status, weak chiral assignments, mass and Yukawa relation, antimatter partner, and observed interaction pattern. Listing these as input properties is not deriving them.

What is supplied and what is predicted

The Standard Model fixes relationships among interactions after one specifies its field content, symmetries, and measured parameters. Many masses and mixing angles are empirical inputs. The 401 atlas is an accurate map of those rules and values; it does not claim a first-principles derivation of why each field exists.

Where the course stops

The 25-card inventory groups gauge directions and one Higgs multiplet by an explicit convention, while the earlier 58 explorer exposes more components. Further mathematical work would use representations, Lagrangians, symmetry breaking, amplitudes, renormalization, and experimental uncertainties. The conceptual course prepares you to recognize what each calculation would need.

From a field card to a testable process
Choose external statesCheck spin, charge, colorPropose permitted vertices
Check energyCombine diagram amplitudesCompare predicted rates with data

The property sheet is a starting point; it cannot replace a complete amplitude calculation.

Takeaway: Use the atlas to ask sharper questions, and distinguish measured inputs from derived results.

Check your understanding

What is a first test of a proposed process?

  1. Check its charges and allowed couplings
  2. Assume all fields convert freely
  3. Count only the number of lines in one diagram
Answer and explanation

Check its charges and allowed couplings

Charges and coupling rules constrain possible vertices.

Does one allowed diagram determine the measured probability alone?

  1. No; other amplitudes, phase space, and parameters matter
  2. Yes; a drawing is a measured trajectory
  3. Yes; spin fixes the complete rate
Answer and explanation

No; other amplitudes, phase space, and parameters matter

A physical prediction combines amplitudes and kinematics.

Are muon and electron excitations of the same field?

  1. No; distinct field descriptions couple in weak decay
  2. Yes; only energy changes
  3. Yes; all leptons form one particle field
Answer and explanation

No; distinct field descriptions couple in weak decay

Muon decay involves distinct lepton fields and neutrino states.

Which electron property helps rule out a direct gluon vertex?

  1. It is a color singlet
  2. It has mass 0.511 MeV
  3. It has an antiparticle
Answer and explanation

It is a color singlet

A direct gluon vertex requires color.

Does listing the electron mass as an input derive that mass?

  1. No; derivation requires a rule that fixes it
  2. Yes; every measured card value is a prediction
  3. Yes; a field name is a mass formula
Answer and explanation

No; derivation requires a rule that fixes it

Input parameters are not predictions from the theory’s deeper rules.

Why is 25 a convention here?

  1. Multiplets and gauge components can be grouped at different resolutions
  2. Because only 25 excitations exist in the universe
  3. Because there are exactly 25 independent species
Answer and explanation

Multiplets and gauge components can be grouped at different resolutions

The atlas declares how it groups degrees of freedom.

Use the interactive trainer for demonstrations, the field explorer, and saved checkpoint progress.