Quantum Cosmological Multidimensional Einstein-Yang-Mills Model in a $R\times S^3\times S^d$ Topology

Abstract

The quantum cosmological version of the multidimensional Einstein-Yang-Mills model in a $R\times S^3\times S^d$ topology is studied in the framework of the Hartle-Hawking proposal. In contrast to previous work in the literature, we consider Yang-Mills field configurations with non-vanishing 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 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.

Plain Latex. Version that appeared in the October 15th, 1997 issue of Physical Review D

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• Collapsing Shells and Black Holes: a quantum analysis
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