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The quantum cosmological version of the multidimensional Einstein-Yang-Millsmodel in a $R \times S^3 \times S^d$ topology is studied in the framework ofthe Hartle-Hawking proposal. In contrast to previous work in the literature, weconsider Yang-Mills field configurations with non-vanishing time-dependentcomponents in both $S^3$ and $S^d$ spaces. We obtain stable compactifyingsolutions that do correspond to extrema of the Hartle-Hawking wave function ofthe Universe. Subsequently, we also show that the regions where 4-dimensionalmetric behaves classically or quantum mechanically (i.e. regions where themetric is Lorentzian or Euclidean) will depend on the number, $d$, of compactspace dimensions.Comment: Plain Latex. Version that appeared in the October 15th, 1997 issue of  Physical Review

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Quantum cosmological multidimensional Einstein-Yang-Mills model in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold">R</mml:mi><mml:mo>×</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>×</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>topology

Quantum cosmological multidimensional Einstein-Yang-Mills model in anR×S3×Sdtopology