Quantum cosmological multidimensional Einstein-Yang-Mills model in an R x S-3 x S-d topology

The quantum cosmological version of the multidimensional Einstein-Yang-Mills model in an R X S-3 X S-d topology is studied in the framework of the Hartle-Hawking proposal. In contrast with previous work in the literature, we consider Yang-Mills field configurations with nonvanishing time-dependent components in both S-3 and S-d spaces. We obtain stable compactifying solutions that do correspond to extrema of the Hartle-Hawking wave function of the Universe. Subsequently, we also show that the regions where the 4-dimensional metric behaves classically or quantum mechanically (i.e., regions where the metric is Lorentzian or Euclidean) will depend on the number d of compact space dimensions. [S0556-2821(97)08220-9].