  The first-order bremsstrahlung emission spectrum is $\alpha d\omega/\omega$
at zero temperature. If the radiation is emitted into a region that contains a
thermal distribution of photons, then the rate is increased by a factor
$1+N(\omega)$ where $N(\omega)$ is the Bose-Einstein function. The stimulated
emission changes the spectrum to $\alpha Td\omega/\omega^{2}$ for $\omega\ll
T$. If this were correct, an infinite amount of energy would be radiated in the
low frequency modes. This unphysical result indicates a breakdown of
perturbation theory. The paper computes the bremsstrahlung rate to all orders
of perturbation theory, neglecting the recoil of the charged particle. When the
perturbation series is summed, it has a different low-energy behavior. For
$\omega\ll\alpha T$, the spectrum is independent of $\omega$ and has a value
proportional to $d\omega/\alpha T$ .
