A Note on Hartle-Hawking Vacua

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.