  The purpose of this note is to establish the basic properties--- regularity
at the horizon, time independence, and thermality--- of the generalized
Hartle-Hawking vacua defined in static spacetimes with bifurcate Killing
horizon admitting a regular Euclidean section. These states, for free or
interacting fields, are defined by a path integral on half the Euclidean
section. The emphasis is on generality and the arguments are simple but formal.
