Physic Labs

Particle physics

Feynman diagrams and the S-matrix

Inspect the inner structure of a Feynman diagram — vertices and propagator — then vary the coupling strength and the energy scale to see how the amplitude behaves, M∝e\mathcal{M} \propto e per vertex and ∝1/q2\propto 1/q^2 through the propagator.

Research

Equipment

  • Rotatable 3D canvas drawing fermion lines and the wavy exchanged-boson line
  • “Strength” slider — the vertex coupling
  • “Energy scale” slider — the momentum transfer
  • “Pause” and “Reset view” buttons

Procedure

  1. Rotate and identify the diagram's parts

    Drag the canvas to rotate the view: identify the two incoming and outgoing fermion lines and the wavy exchanged-boson line joining the two vertices. Each vertex is an emission or absorption event; press “Reset view” if you lose orientation.

  2. Vary the coupling and reason about the perturbative series

    Drag “Strength” and pause to inspect a vertex. With two vertices the amplitude scales as e2e^2, i.e. the fine-structure constant α=e2/(4πε0ℏc)≈1/137\alpha = e^2/(4\pi\varepsilon_0\hbar c) \approx 1/137; deduce why higher-order diagrams contribute progressively less.

  3. Change the energy scale and the propagator's role

    Sweep “Energy scale” to change the momentum transfer qq carried by the virtual boson. Recall the photon propagator behaves as 1/q21/q^2: small-momentum-transfer processes dominate. Compare with a diagram you draw by hand, assigning each element a factor in M\mathcal{M}.

Simulation

Experiment history

In 1949 Richard Feynman published his spacetime diagrams in “The Theory of Positrons” and “Space-Time Approach to Quantum Electrodynamics”, turning the cumbersome QED calculation into intuitive rules attached to a picture. Freeman Dyson proved the same year that Feynman's method was equivalent to the operator formalisms of Julian Schwinger and Sin-Itiro Tomonaga; the three shared the 1965 Nobel prize. The S-matrix concept — the operator connecting asymptotic in- and out-states — was proposed by John Wheeler in 1937 and developed by Werner Heisenberg in 1943. Feynman diagrams are precisely the language computing each term of the S-matrix in a perturbative series, and today they extend to all Standard Model interactions.

Related physicists

Richard FeynmanPaul DiracJulian Seymour SchwingerSin-Itiro Tomonaga

Related library topics

Feynman diagrams and the S-matrix