  The standard derivations of electromagnetic energy and momentum in media take
Maxwell's equations as the starting point. It is well known that for dispersive
media this approach does not directly yield exact expressions for the energy
and momentum densities. Although Maxwell's equations fully describe
electromagnetic fields, the general approach to conserved quantities in field
theory is not based on the field equations, but rather on the action. Here an
action principle for macroscopic electromagnetism in dispersive, lossless media
is used to derive the exact conserved energy-momentum tensor. The time-averaged
energy density reduces to Brillouin's simple formula when the fields are
monochromatic. The momentum density is not given by the familiar Minkowski
expression $\mathbf{D}\times\mathbf{B}$, even for time-averaged monochromatic
fields. The results are unaffected by the debate over momentum balance in
light-matter interactions.
