Topology Change in (2+1)-Dimensional Gravity

Abstract

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial topology change are nonvanishing---in fact, they can be infrared divergent---but that they are infinitely suppressed relative to similar topology-preserving amplitudes.

19 pages of text plus 4 pages of figures, LaTeX (using epsf), UCD-11-94

References in corpus (2)

• Six ways to quantize (2+1)-dimensional gravity
• Topology change in ISO(2,1) Chern-Simons gravity

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