TOPOLOGICAL KINK SOLITON — φ⁴ Field Theory

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Q = +1
φ(x,t) — field (φ=±1 vacua, kink interpolates)
V(φ) = (φ²−1)²/4 — Mexican hat potential (1D)
φ⁴ kink: φ(x,t) = tanh((x−x₀)/√2·γ), topological charge Q = ½(φ(+∞)−φ(−∞)) = ±1. Kinks are topologically stable — cannot unwind continuously. Kink+antikink annihilate, releasing energy as radiation. Lorenz-boosted: γ = 1/√(1−v²). Kink mass M = 2√2/3. Relativistic field equation: φ̈−φ''+φ³−φ = 0.