Topological Kink — φ⁴ Field Theory

Solitons that cannot be continuously deformed to the vacuum

Field Parameters

Setup

Energy E = 0.00
Topological charge Q = 0
Kink position x₀ =
Physics: The φ⁴ theory with V(φ) = λ/4·(φ²−m²/λ)² has two degenerate vacua φ = ±v₀ = ±m/√λ. A kink is a static solution φ_K(x) = v₀·tanh((x−x₀)/ξ) interpolating between the two vacua. Its width ξ = √(2/m²). Kinks carry a conserved topological charge Q = (φ(+∞)−φ(−∞))/(2v₀) = ±1, which cannot change under smooth evolution — they are topologically protected. Kink-antikink pairs annihilate via breather modes. The mass (rest energy) of a kink is E_K = (4/3)·m³/λ. Relativistic Lorentz contraction occurs at high velocity.