Factor Sequences in Quantized General Relativity

The problem of the order of factors in the constraint equations of general relativity has been investigated. Although the constraints plus Hamiltonian form a factor group in the nonquantized version of the theory, it does not follow directly that they will do so in the quantized version. The difficulty lies in the fact that the commutator of two expressions depends upon the order of factors chosen for them. We have explicitly exhibited a class of factor sequences for the constraints such that they do indeed form a factor group.