= Electromagnetic coupling of a sine-Gordon topological current
{title2=$j^\mu=(\theta_x,-\theta_t),\quad Q=\int\theta_x\,dx$}
The identically conserved <topological current> $j$ couples to an external electromagnetic <gauge potential> through $-A_\mu j^\mu=-A_0\theta_x+A_1\theta_t$. A <gauge transformation> changes this coupling only by a divergence. The <Euler-Lagrange field equation> becomes $\theta_{tt}-\theta_{xx}+\sin\theta+E=0$, with $E=\partial_tA_1-\partial_xA_0$. A unit <Sine-Gordon kink> has unnormalized charge $Q=2\pi$ and mass $8$. For spatially uniform forcing, its field momentum balance is $\dot P=QE$ when the boundary stress contributions cancel.
Back to article page
