Canonical quantization with quadratic constraints

Based on an analysis first suggested by Bryce S. DeWitt, we have found that a special case of the general classical theory involving quadratic constraints can be quantized canonically, in the sense that the quantum constraints are consistent. In particular, this special case contains all known physical theories of bosons,including Einstein'sGeneral Theory of Relativity. The quantum constraints for this theory are given explicitly in an appendix.