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Simplicial Quantum Gravity From Two to Four Dimensions

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Probabilistic Methods in Quantum Field Theory and Quantum Gravity

Part of the book series: NATO ASI Series ((NSSB,volume 224))

Abstract

Recent work on Regge’s lattice formulation of quantum gravity is reviewed. The problem of the lattice transcription of the action and the measure is discussed, and a comparison is made to the expected results in the continuum. The recovery of general coordinate invariance in the continuum is illustrated in the two-dimensional case, where critical exponents can be compared to the exact continuum conformal field theory results of KPZ. In four dimensions the lattice results strongly suggest that the pure Einstein theory is not defined even at the non-perturbative level. The addition of higher derivative terms in the pure gravity theory appears to cure the unboundedness problem, but the nature of the ground state and the fixed point structure remains an open question.

Invited lecture presented at the Cargèse NATO workshop on ‘Probabilistic Methods in Field Theory and Quantum Gravity’, August 1989. This work supported in part by the National Science Foundation under grants NSF-PHY-8605552 and NSF-PHY-8906641

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Author information

Authors and Affiliations

  1. Department of Physics, University of California, Irvine, CA, 92717, USA

    Herbert W. Hamber

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  1. Herbert W. Hamber
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Editors and Affiliations

  1. The Niels Bohr Institute, Copenhagen, Denmark

    P. H. Damgaard

  2. University of Vienna, Vienna, Austria

    H. Hüffel

  3. Utah State University, Logan, Utah, USA

    A. Rosenblum

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Hamber, H.W. (1990). Simplicial Quantum Gravity From Two to Four Dimensions. In: Damgaard, P.H., Hüffel, H., Rosenblum, A. (eds) Probabilistic Methods in Quantum Field Theory and Quantum Gravity. NATO ASI Series, vol 224. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3784-7_17

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  • DOI: https://doi.org/10.1007/978-1-4615-3784-7_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6686-7

  • Online ISBN: 978-1-4615-3784-7

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