Interacting Klein–Gordon fields: ψ and its mediator φ

The simulation evolves the coupled equations ψ̈ = ψ″ − (mψ² + gφ)ψ and φ̈ = φ″ − mφ²φ − g|ψ|². The complex field carries a U(1) charge in the undamped bulk; the real mediator is sourced by |ψ|². The lower panels show a rolling space–time history of the charge density and of the mediator field.

positive charge / primary curve negative charge / secondary curve |ψ|² or positive φ heat negative φ / absorbing layers

Scenario

Display

18 integration steps / frame
×1 visible time span

Physical parameters

Changing these sliders restarts the selected scenario so that φ is recomputed consistently.

Diagnostics

What to look for

The orange density |ψ|² sources a negative mediator well φ. This lowers m²eff = mψ² + gφ around the packet and can help localize it. The new lower panels let you see immediately whether the packet is moving, breathing, radiating, or dispersing.