The φ⁴ scalar field theory has topological soliton solutions: φ(x,t) = tanh((x − vt)/√2 · 1/√(1−v²)), interpolating between vacuum states ±1. These kinks carry topological charge and survive collisions. Explore kink-antikink scattering, energy density profiles, and the double-well potential landscape.
Key facts:
• Vacuum: φ = ±1, potential V = (φ²−1)²/4
• Kink mass: M = 2√2/3 ≈ 0.943
• Topological charge: Q = [φ(+∞)−φ(−∞)]/2
• At low velocity, kinks form bound states (bions)
• At high velocity, kinks pass through each other
• Annihilation threshold ~v ≈ 0.26 (resonance windows exist)
• Energy is Lorentz-contracted: soliton width ∝ √(1−v²)