Using MOSFET’s For AC Rectification
It is possible to create a very efficient rectifier with a MOSFET - but not by just connecting the Gate to the Drain! 

All discrete MOSFETs have an inherent reverse 'body' diode between Source and Drain. This diode is as good as normal silicon rectifier, so the FET will work quite well as a rectifier provided that it is not turned on at the wrong time (ie. when the Drain voltage is positive relative to the Source, since that would nullify the blocking effect of the body diode). 

If the Gate is left floating then it might pick up a static charge causing the FET to turn on continuously, which is obviously bad news. However if the FET is only turned on when Source-Drain voltage is negative then it will bypass the body diode and cut losses to almost zero. The trick is to synchronize the Gate drive to the incoming AC voltage.