Einstein-Maxwell theory in 2+1 dimensions

Einstein-Maxwell theory in 2+1 dimensions is considered as a toy model for the 3+1 theory and as a means for understanding field theories without a background space-time geometry. Two possible approaches to the quantization of this theory are presented, one based on a Schwinger-Tomonaga time evolution equation and the other on a loop space construction, and the problems arising in both of these are discussed.