Multidimensional classical and quantum cosmology with intersecting p-branes

A multidimensional cosmological model describing the evolution of (n+1) Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane ansatz is adopted the field equations are reduced to the equations for the Toda-like system. The Wheeler–De Witt equation is obtained. In the case when n “internal” spaces are Ricci-flat, one space M0 has a non-zero curvature, and all p-branes do not “live” in M0; the classical and quantum solutions are obtained if certain orthogonality relations on parameters are imposed. Spherically symmetric solutions with intersecting non-extremal p-branes are singled out. A non-orthogonal generalization of intersection rules corresponding to (open, closed) Toda lattices is obtained. A chain of bosonic D⩾11 models (that may be related to hypothetical higher dimensional supergravities and F-theories) is suggested.