In this work, I review some aspects concerning the evolution of quantum lowenergy fields in a foamlike spacetime, with involved topology at the Planck scale but with a smooth metric structure at large length scales, as follows. Quantum gravitational fluctuations may induce a minimum length thus introducing an additional source of uncertainty in physics. The existence of this resolution limit casts doubts on the metric structure of spacetime at the Planck scale and opens a doorway to nontrivial topologies, which may dominate Planck scale physics. This foamlike structure of spacetime may show up in low-energy physics through loss of quantum coherence and mode-dependent energy shifts, for instance, which might be observable. Spacetime foam introduces nonlocal interactions that can be modeled by a quantum bath, and low-energy fields evolve according to a master equation that displays such effects. Similar laws are also obtained for quantum mechanical systems evolving according to good real clocks, although the underlying Hamiltonian structure in this case establishes serious differences among both scenarios. Contents.— Quantum fluctuations of the gravitational field; Spacetime foam; Loss of quantum coherence; Quantum bath; Low-energy effective evolution; Real clocks; Conclusions. Int. J. Mod. Phys. A14 (1999) 4079–4120

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Quantum evolution in space-time foam

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.

Multidimensional Classical and Quantum Wormholes in Models with Cosmological Constant

Space-time wormholes with Yang-Mills fields

Quantum wormholes in Kantowski-Sachs spacetime

We solve the Euclidean Einstein equations with three-index antisymmetric and two-index antisymmetric (electromagnetic) tensors for monopole configurations on a space with three-surfaces of topology {ital S}{sup 1}{times}{ital S}{sup 2} and describe wormhole solutions. We show that these wormholes and the one of Giddings and Strominger, Hawking, Halliwell and Laflamme, and Myers can be obtained by slicing five-dimensional spaces with horizons.

Brian J. Keay

Papers

S1 >= 2 wormholes.