= Lagrangian
{disambiguate=field theory}
{c}
{title2=$S[\phi]=\int d^dx\,\mathcal L(\phi,\partial\phi,x)$}
{wiki}
Lagrangian field theory specifies an <action> by integrating a Lagrangian density $\mathcal L(\phi,\partial\phi,x)$ over spacetime. Requiring its <first variation> to vanish for compactly supported field variations yields the field <Euler-Lagrange equations>. The variational <Lagrangian> is the integrand, whereas this field-theoretic formalism specifies the continuum fields and their dynamics.
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