Quantum evolution across singularities: the case of geometrical resolutions

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.

25 pages, 1 figure

References in corpus (4)

• On the Quantum Resolution of Cosmological Singularities using AdS/CFT
• Effective Dynamics of the Matrix Big Bang
• From Big Crunch to Big Bang with AdS/CFT
• Toward the End of Time

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• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Holographic Curvature Perturbations in a Cosmology with a Space-Like Singularity
• Null cosmological singularities and free strings
• Aspects of Plane Wave (Matrix) String Dynamics
• Quantum Quench in $c=1$ Matrix Model and Emergent Space-times
• Following the density perturbations through a bounce with AdS/CFT Correspondence
• Notes on quantum evolution across singularities
• Old and New Scaling Laws in Quantum Quench