Mechanism for radiating power when accelerating charged particles On reading through selection rules constraining transitions from one state to another, it states:

Thus, there is no E0 (electric monopoles) or M0 (magnetic monopoles,
  which do not seem to exist) radiation.

But when describing Larmor radiation, is this not a simple example of electric monopoles (e.g. electrons) radiating power? Perhaps the fundamental question is: what is the initial and final state when describing Larmor radiation from a quantum mechanical perspective? 
 A: The radiation produced by a charge accelerating in otherwise empty space is not called monopole radiation. Monopole radiation (if it existed) would be the name for radiation associated with an oscillating or otherwise accelerating monopole moment. This would be a spherically symmetric charge distribution accelerating or oscillating in a spherically symmetric fashion. However, such oscillation does not excite electromagnetic waves.
When an electron accelerates in otherwise empty space, the electron can be correctly called a monopole, but the change in the charge distribution as a function of time is not spherically symmetric, so the associated radiation is not monopole radiation. In fact it is mainly dipole radiation, and also contains higher order terms.
To make this precise, just set up a system of coordinates with a fixed origin and define the various multipole moments in the standard way from the distribution of charge relative to this origin of coordinates. In the case of an accelerating point charge it is easy to see that all these multipole moments are changing with time. For example the dipole moment, relative to the given, fixed origin, is
$$
{\bf d}(t) = -e {\bf x}(t)
$$
where $\bf x$ is the location of the electron.
This changing dipole moment doesn't mean the electron is changing internally in any sense; it does mean that the location of the charge provided by the electron is changing.
A: You need to specify what you are dealing with. The selection rules are usually talked about in the context of transitions in atoms, molecules, or solid state systems, like crystals. In each case selection rules are different. "No electric monopoles", I think, simply refers to the fact that we usually only talk about spectroscopy on neutral (non-charged) atoms/molecules.
Emission of light by accelerated charged particles, presumably free particles, is of course an example of emission by a monopole. There the "selection rules" would probably be the conservation of energy & momentum. As a result you will probably find that charged particle in free space cannot emit light (due to "selection rules"). However, if there is something to break the translational invariance of the space-time, e.g. an externally applied field, then light emission could occur.
------------ In response to comment
I did not say that accelerated charge does not radiate. If there is something to accelerate the charge, there will be no translational invariance so there is no problem with radiation. What I said, is that an electron in free-space will not suddenly emmit light and accelerate/decelerate. Now that, is due to translational invariance and conservation of momentum (see Noether's theorem).
Regarding the polarization of emission in case of falling onto, say, a planet. Yes, there most likely will be a specific limitation on the allowed state of polarization, but this will be very specific to problem at hand. The whole problem will have some specific symmetries (e.g. cyllindrical symmetry, if your charged particle is falling onto a planet head-on (no orbiting)). These symmetries can be combined into a group. Then the emitted field would have to be invariant under the actions of this symmetry group. In general this is the subject of representation theory. In most cases, physicists proceed by intuition, but when it is not enough, the representation theory provides a very robust framework for handling these 'selection rule' problems. 
