  We derive an exact, continuous-variable path integral (PI) representation of
the canonical partition function for electronically nonadiabatic systems.
Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements
of the Boltzmann operator are expressed in Cartesian coordinates for both the
nuclear and electronic degrees of freedom. The PI discretization presented here
properly constrains the electronic Cartesian coordinates to the physical
subspace of the mapping. We numerically demonstrate that the resulting PI-ST
representation is exact for the calculation of equilibrium properties of
systems with coupled electronic and nuclear degrees of freedom. We further show
that the PI-ST formulation provides a natural means to initialize semiclassical
trajectories for the calculation of real-time thermal correlation functions,
which is numerically demonstrated in applications to a series of nonadiabatic
model systems.
