Field variation
= Field variation
{title2=$\delta_0\phi(x)=\phi\prime(x)-\phi(x)$}
A fixed-coordinate <field variation> compares two <fields> at the same <spacetime> point. If a transformation also changes coordinates by $\delta x^\mu$, its total variation and fixed-coordinate variation differ by $\delta x^\mu\partial_\mu\phi$. Keeping these separate is essential when applying the <Noether current for a spacetime symmetry>.