Is it technically correct to place speakers behind your audience? What are the rules for loudspeaker placement in an auditorium?
Placing the main speakers behind the audience would create a very unnatural feel for the audience. The sound should seem to come from the direction of the person speaking, the band, etc on the stage.
Unfortunately there is no easy answer to loudspeaker placement. In general auditorium acoustics is a very complex field. It involves the interaction of the various sound sources which create constructive and destructive interference at various frequencies at various distances from the sources. Sound reflections from the room walls and various objects in the room also play a big factor. The room design and sound absorbing material placement is just as important as the sound system itself, if not more important.
In larger auditoriums/stadiums sound propagation delay (the time it takes the sound to reach the listener) can become a big factor requiring specialized equipment to delay individual drivers/speakers.
Art Noxon, an acoustical engineer, covers some of the main aspects here:
At the very least I would definitely place the main speakers up front!
There is no technical reason you could not, however there is a perceptual reason you might not want to. People can tell the direction that sound is coming from. If you place speakers in the back of the room, it will sound like sound coming from them is coming from the back of the room. If that is desirable, then you would want to do so.
Additionally, there are speaker array setups that place speakers, facing towards listeners, but spacing them out around the room so that the back can still hear without deafening the front. These array based systems integrate delays in to the speakers further back such they produce their sound at the same time that the sound from the front speakers is passing them. In this way, it is possible to evenly cover a space in sound in order to deal with how rapidly sound intensity falls off with distance from a speaker.
As Qrchack point's out, line arrays at the front of the room can also often have a similar impact (depending on room layout) so it isn't always necessary to position speakers elsewhere for this purpose, but placing delay speakers in the array around the room is a good option for troubleshooting problem spots that can't be covered with a line array or when placing those speakers may be cheaper than building a line array (or extreme control of SPL(volume) is needed.)