Lorentzian path integral for minisuperspace cosmology

The path integral for minisuperspace models of cosmology is defined as a sum over Lorentzian geometries, and is a Green function for the Wheeler-DeWitt operator. It is shown to be a symmetric function of the initial and final configurations, and its real part is a solution to the Wheeler-DeWitt equation. The Lorentzian path integral is computed explicitly for the de Sitter minisuper-space model and is convergent. The resulting Green function is then related to the solutions of the Wheeler-DeWitt equation known as the Hartle-Hawking and tunneling wave functions of the Universe. The real part of this Green function is a product of Hartle-Hawking wave functions.