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Quantum evolution across singularities: the case of geometrical resolutions

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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.
Keywords
m(atrix) theories, penrose limit and pp-wave background, spacetime singularities, COHERENT STATES, MODELS

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Please use this url to cite or link to this publication:

MLA
Craps, Ben, Frederik De Roo, and Oleg Evnin. “Quantum Evolution Across Singularities: The Case of Geometrical Resolutions.” JOURNAL OF HIGH ENERGY PHYSICS 4 (2008): 036–1–036–25. Print.
APA
Craps, B., De Roo, F., & Evnin, O. (2008). Quantum evolution across singularities: the case of geometrical resolutions. JOURNAL OF HIGH ENERGY PHYSICS, (4), 036–1–036–25.
Chicago author-date
Craps, Ben, Frederik De Roo, and Oleg Evnin. 2008. “Quantum Evolution Across Singularities: The Case of Geometrical Resolutions.” Journal of High Energy Physics (4): 036–1–036–25.
Chicago author-date (all authors)
Craps, Ben, Frederik De Roo, and Oleg Evnin. 2008. “Quantum Evolution Across Singularities: The Case of Geometrical Resolutions.” Journal of High Energy Physics (4): 036–1–036–25.
Vancouver
1.
Craps B, De Roo F, Evnin O. Quantum evolution across singularities: the case of geometrical resolutions. JOURNAL OF HIGH ENERGY PHYSICS. 2008;(4):036–1–036–25.
IEEE
[1]
B. Craps, F. De Roo, and O. Evnin, “Quantum evolution across singularities: the case of geometrical resolutions,” JOURNAL OF HIGH ENERGY PHYSICS, no. 4, pp. 036-1-036–25, 2008.
@article{595664,
  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.},
  author       = {Craps, Ben and De Roo, Frederik and Evnin, Oleg},
  issn         = {1126-6708},
  journal      = {JOURNAL OF HIGH ENERGY PHYSICS},
  keywords     = {m(atrix) theories,penrose limit and pp-wave background,spacetime singularities,COHERENT STATES,MODELS},
  language     = {eng},
  number       = {4},
  pages        = {036-1--036-25},
  title        = {Quantum evolution across singularities: the case of geometrical resolutions},
  url          = {http://dx.doi.org/10.1088/1126-6708/2008/04/036},
  year         = {2008},
}

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