UB-ECM-PF 92/33 hep-th/9312132 December 1992 Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom induced by quantum elds is considered, for spacetimes with nontrivial topology of the kind R 1 T, for varying D. It is shown that a dynamical origin for the Lorentzian signature is possible in the ve-dimensional space R T with small torus radius (periodic boundary conditions), as well as in four-dimensional space with trivial topology. Hence, the possibility exists that the early universe might have been of the Kaluza-Klein type, i.e. multidimensional and of Lorentzian signature. E-mail: eli @ ebubecm1.bitnet On leave from Tomsk Pedagogical Institute, 634041 Tomsk, Russian Federation. E-mail: odintsov @ ebubecm1.bitnet