The problem of time in quantum gravity

RAFAEL FERRARO

GRAVITATION & COSMOLOGY

Springer

Año: 1999 vol. 5 p. 195 - 198

0202-2893

The inner product turning the space of solutions of the Wheeler-DeWitt (WDW) equation into a Hilbert space is still unknown. Attempts of building this Hilbert space by looking for a time in the configuration space are frequent in the literature (especially in minisuperspace models). They exploit the resemblance between the WDW equation and the Klein_Gordon equation. However it is known that the similarity between geometrodynamics and relativistic particle dynamics is not strong enough for quantizing both systems in the same way. We propose a different mechanical simile for geometrodynamics which has an “extrinsic” time (associated with the canonical momenta) instead of an “intrinsic” one, and show how to manage the solutions of the “WDW” equation in order to correctly quantize the system.