Particle physics
Renormalization in quantum field theory
Explore the idea of renormalization: the measured coupling 'runs' with the energy scale μ. Adjust the interaction strength and the scale μ/μ₀ on the 3D model to see the amplitude and the vacuum value v change with scale.
Equipment
- 3D potential/field surface representing a scale-dependent system
- Strength slider (10–200)
- Energy-scale slider μ/μ₀
- Pause and Reset-view buttons; readouts for A, v, μ/μ₀
Procedure
Observe the potential surface
Leave the sliders at mid-range and rotate the canvas: the surface illustrates the effective parameters of a field theory. Read the relative amplitude A and vacuum value v — these are the measurable quantities after renormalization.
Change the energy scale
Sweep the scale slider μ/μ₀ from low to high: the readouts show the parameters 'running' — a coupling measured at different energies takes different values because loop integrals depend on μ. This is the physical meaning of the beta function .
Compare strengths and predict
Set the strength low then high at fixed μ/μ₀: the vacuum value v shifts and amplitude A changes — the analog of redefining a 'bare' coupling. Predict the parameter at μ/μ₀ = 2 before reading it; press 'Reset view' if you lose orientation.