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arXiv · 0801.4536

Quantum evolution across singularities: the case of geometrical resolutions

Ben Craps·Frederik De Roo·Oleg Evnin
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Abstract

We continue the study of time-dependent Hamiltonians with an isolated singularity in their time dependence, describing propagation on singular space-times. In previous work, two of us have proposed a "minimal subtraction" prescription for the simplest class of such systems, involving Hamiltonians with only one singular term. On the other hand, Hamiltonians corresponding to geometrical resolutions of space-time tend to involve multiple operator structures (multiple types of dependence on the canonical variables) in an essential way. We consider some of the general properties of such (near-)singular Hamiltonian systems, and further specialize to the case of a free scalar field on a two-parameter generalization of the null-brane space-time. We find that the singular limit of free scalar field evolution exists for a discrete subset of the possible values of the two parameters. The coordinates we introduce reveal a peculiar reflection property of scalar field propagation on the generalized (as well as the original) null-brane. We further present a simple family of pp-wave geometries whose singular limit is a light-like hyperplane (discontinuously) reflecting the positions of particles as they pass through it.

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Ben Craps, Frederik De Roo, Oleg Evnin. 2008-01-29. Quantum evolution across singularities: the case of geometrical resolutions. https://doi.org/10.1088/1126-6708%2F2008%2F04%2F036

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