  Hartle's generalized quantum mechanics in the sum-over-histories formalism is
used to describe a nonabelian gauge theory. Predictions are made for certain
alternatives, with particular attention given to coarse-grainings involving the
constraint. In this way, the theory is compared to other quantum-mechanical
descriptions of gauge theories in which the constraints are imposed by hand.
The vanishing of the momentum space constraint is seen to hold, both through a
simple formal argument and via a more careful description of the Lorentzian
path integral as defined on a spacetime lattice. (Incidentally, the treatment
of the time slicing in the path integral may be of general technical interest.)
The configuration space realization of the constraint is shown to behave in a
more complicated fashion. For some coarse grainings, we recover the known
result from an abelian theory, that coarse grainings by values of the
constraint either predict its vanishing or fail to decohere. However, sets of
alternatives defined in terms of a more complicated quantity in the abelian
case are exhibited where definite predictions can be made which disagree with
the assumption that the constraints vanish. Finally, the configuration space
sum-over-histories theory is exhibited in a manifestly Lorentz-invariant
formulation.
