Hamiltonian density
= Hamiltonian density
{c}
{title2=$\mathcal H=\pi_a\dot\phi_a-\mathcal L$}
A <Hamiltonian density> is a local integrand for the field-theory <Hamiltonian>. For canonical fields with invertible velocity-momentum relation it is the <Legendre transform in mechanics> of the <Lagrangian density>, summing over all conjugate field components. <Gauge theories> require constraints and multiplier terms as well.