A. Zee, Quantum Field Theory in a Nutshell · Problem V.6.2

Field Theory Redux

Physics — QFT

Problem

Discuss the solitons in the so-called sine-Gordon theory L=12(∂φ)2−gcos⁡(βφ)\mathcal{L} = \frac{1}{2}(\partial\varphi)^2 - g\cos(\beta\varphi). Find the topological current. Is the Q=2Q = 2 soliton stable or not?

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