Multidimensional Classical and Quantum Wormholes in Models with Cosmological Constant

A multidimensional cosmological model with space-time consisting of $n (n \ge 2)$Einsteinspaces$M_{i}$ is investigated in the presence of a cosmological constant $\mathrm{\Lambda }$ and a homogeneous minimally coupled scalar field $\phi (t)$ as a matter source. Classical and quantum wormhole solutions are obtained for $\mathrm{\Lambda }<0$ and all $M_i$ being Ricci-flat. Classical wormhole solutions are also found for $\mathrm{\Lambda }<0$ and only one of the $M_i$ being Ricci-flat for the case of spontaneous compactification of the internal dimensions with fine tuning of parameters.