  Surprisingly, there exists a quantum flux-side time-correlation function
which has a non-zero short-time (t->0+) limit, and thus yields a rigorous
quantum generalization of classical transition-state theory (TST). In this Part
I of two articles, we introduce the new time-correlation function, and derive
its short-time limit. The new ingredient is a generalized Kubo transform which
allows the flux and side dividing surfaces to be the same function of
path-integral space. Choosing this common dividing surface to be a single point
gives a short-time limit which is identical to an expression introduced on
heuristic grounds by Wigner in 1932, but which does not give positive-definite
quantum statistics, causing it to fail while still in the shallow-tunnelling
regime. Choosing the dividing surface to be invariant to imaginary-time
translation gives, uniquely, a short-time limit that gives the correct
positive- definite quantum statistics at all temperatures, and which is
identical to ring-polymer molecular dynamics (RPMD) TST. We find that the
RPMD-TST rate is not a strict upper bound to the exact quantum rate, but a good
approximation to one if real-time coherence effects are small. Part II will
show that the RPMD-TST rate is equal to the exact quantum rate in the absence
of recrossing.
