  A systematic field-theory approach to Electron Spin Resonance (ESR) in the
$S=1/2$ quantum antiferromagnetic chain at low temperature $T$ (compared to the
exchange coupling $J$) is developed. In particular, effects of a transverse
staggered field $h$ and an exchange anisotropy (including a dipolar
interaction) $\delta$ on the ESR lineshape are discussed. In the lowest order
of perturbation theory, the linewidth is given as $\propto Jh^2/T^2$ and
$\propto (\delta/J)^2 T$, respectively. In the case of a transverse staggered
field, the perturbative expansion diverges at lower temperature;
non-perturbative effects at very low temperature are discussed using exact
results on the sine-Gordon field theory. We also compare our field-theory
results with the predictions of Kubo-Tomita theory for the high-temperature
regime, and discuss the crossover between the two regimes. It is argued that a
naive application of the standard Kubo-Tomita theory to the
Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and
exact identity on the polarization dependence is derived for certain class of
anisotropy, and compared with the field-theory results.
