= Sine-Gordon theory
{c}
{title2=$\mathcal L=\frac12(\partial\varphi)^2-\frac{m^2}{\beta^2}(1-\cos\beta\varphi)$}
A relativistic <real scalar field> theory with a periodic cosine potential. In physical coordinates $y^\mu$, one normalization is $\mathcal L=\tfrac12\partial_\mu\varphi\partial^\mu\varphi-m^2(1-\cos\beta\varphi)/\beta^2$. With $\phi=\beta\varphi$ and $x^\mu=my^\mu$, its <action> is $S=\beta^{-2}\int d^2x[\tfrac12(\partial\phi)^2+\cos\phi-1]$. Its <Euler-Lagrange field equation> is the <Sine-Gordon equation>. Distinct <scalar-field vacua> differ by $2\pi$ in $\phi$, permitting a <Sine-Gordon kink>.
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