Multidimensional Classical and Quantum Wormholes in Models with Cosmological Constant

A multidimensional cosmological model with space-time consisting of $n (n \ge 2)$ Einstein spaces $M_{i}$ is investigated in the presence of a cosmological constant $\Lambda$ and a homogeneous minimally coupled scalar field $\varphi(t)$ as a matter source. Classical and quantum wormhole solutions are obtained for $\Lambda < 0$ and all $M_{i}$ being Ricci-flat. Classical wormhole solutions are also found for $\Lambda < 0$ 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.