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An example of such a wave function is the Hartle-Hawking state.
He subsequently developed the research in collaboration with Jim Hartle, and in 1983 they published a model, known as the Hartle-Hawking state.
The concept is useful in cosmology because it can help smooth out gravitational singularities in models of the universe (see Hartle-Hawking state).
The precise form of the Hartle-Hawking state is the path integral over all D-dimensional geometries that have the required induced metric on their boundary.
The Hartle-Hawking state is the wave function of the Universe-a notion meant to figure out how the Universe started-that is calculated from Feynman's path integral.
Thus, the Hartle-Hawking state universe has no beginning, but it is not the steady state universe of Hoyle; it simply has no initial boundaries in time nor space.
In theoretical physics, the Hartle-Hawking state, named after James Hartle and Stephen Hawking, is a proposal concerning the state of the universe prior to the Planck epoch.
Newer approaches based in part on the work of DeWitt and Dirac include the Hartle-Hawking state, Regge calculus, the Wheeler-DeWitt equation and loop quantum gravity.
He argues in favor of the Big Bang being interpreted as the temporal beginning of the universe, criticizing models which suggest differently, such as the Cyclic model, vacuum fluctuation models, and the Hartle-Hawking state model.