Quantum Analysis of the Compactification Process in the Multidimensional EinsteinYangMill.pdf

QUANTUM ANALYSIS OF THE COMPACTIFICATION PROCESS IN THE MULTIDIMENSIONAL EINSTEIN-YANG-MILLS SYSTEM O. BERTOLAMI a Departamento de F´ısica, Instituto Superior T´ecnico, Av. Rovisco Pais, Lisbon, Portugal 7 9 P.D. FONSECA 9 1 Department of Physics and Astronomy, Rutgers University, t Piscataway, NJ 08855-0849, U.S.A. c O P.V. MONIZ 7 1 University of Cambridge, DAMTP, Silver Street, v Cambridge CB3 9EW, England 6 3 0 We study solutions of the Wheeler-DeWitt equation obtained when considering homoge- neous and isotropic (up to a gauge transformation) field configurations of the Einstein- 0 Yang-Mills system in D = 4 + d dimensions with an R ×S3 ×Sd topology and assuming 1 the Hartle-Hawking boundary conditions. 7 9 / c 1 Introduction q - r We report in this contribution on the result of recent work on the quantum cosmol- g ogy of the minisuperspace model arising from the coset space dimensional reduction : v of the D-dimensional Einstein-Yang-Mills (EYM) sytem 1. Our method consists in i exploiting the isometries of an homogeneous and isotropic spacetime in four 2,3,4 or X D-dimensions 5 to restrict the possible field configurations. We find that compact- r a ifying solutions correspond to maxima of the