  This dissertation unifies one of the central methods of classical rate
calculation, `Transition-State Theory' (TST), with quantum mechanics, thereby
deriving a rigorous `Quantum Transition-State Theory' (QTST). The resulting
QTST is identical to ring polymer molecular dynamics transition-state theory
(RPMD-TST), which was previously considered a heuristic method, and whose
results we thereby validate. The key step in deriving a QTST is alignment of
the flux and side dividing surfaces in path-integral space to obtain a quantum
flux-side time-correlation function with a non-zero $t\to 0_+$ limit. We then
prove that this produces the exact quantum rate in the absence of recrossing by
the exact quantum dynamics, fulfilling the requirements of a QTST. Furthermore,
strong evidence is presented that this is the only QTST with positive-definite
Boltzmann statistics and therefore the pre-eminent method for computation of
thermal quantum rates in direct reactions.
