  Motivated by recent developments in the field of plasmonics, we develop the
theory of radiation from one-dimensional electron liquids, showing that the
spectrum of thermal radiation emitted from the system exhibits signatures of
non-Fermi liquid behavior. We derive a multipole expansion for the radiation
based on the Tomonaga-Luttinger liquid model. While the dipole radiation
pattern is determined by the conductivity of the system, we demonstrate that
the quadrupole radiation can reveal important features of the quantum liquid,
such as the Luttinger parameter. Radiation offers a probe of the interactions
of the system, including Mott physics as well as non-linear Luttinger liquid
behavior. We show that these effects can be probed in current experiments on
effectively one-dimensional electron liquids, such as carbon nanotubes.
