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NASA NTRS1987

Gauge invariant quantum cosmology

The study of boundary conditions, the Hamiltonian constraint, reparameterization-invariance, and quantum dynamics, is presently approached by means of the path-integral quantization of minisuperspace models. The separation of the wave functions for expansion and contraction by the Feynman boundary conditions is such that there can be no interference between them. This is implemented by the choice of a contour in the complex plane, in order to define the phase of the square-root Arnowitt, Deser, and Misner (1960) Hamiltonian for expansion, collapse, and the classically forbidden region.

Berger, Beverly K.↗

NASA NTRS1972

Minisuperspace.

The model universe in which a Klein-Gordon type equation was first studied is reviewed, as well as a Hamiltonian statement of the corresponding classical problem of solving Einstein's equation. Developments are generalized to a minisuperspace with a nondiagonal metric in place of an appropriate wave equation, in which case minisuperspace is no longer flat. The basic commutation relations for quantization in this curved space are then related to its Killing vectors.

Misner, C. W.↗