Nonperturbative Lorentzian Path Integral for Gravity
Open accessAbstract
We construct a well-defined regularized path integral for Lorentzian quantum gravity in terms of dynamically triangulated causal space-times. Each Lorentzian geometry and its action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time and, for finite lattice volume, the associated transfer matrix is self-adjoint, bounded, and strictly positive. The degenerate geometric phases found in dynamically triangulated Euclidean gravity are not present.
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The alternative Lorentzian model introduced by Ambjørn and Loll has much nicer properties, including a continuum limit that appears numerically to match a finite-sized, spherical semiclassical configuration.
“An alternative “Lorentzian” model, introduced by Ambjørn and Loll [16, 9, 12, 10, 180, 13], however, has much nicer properties, including a continuum limit that appears numerically to match a finite-sized, spherical “semiclassical” configuration.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [9]
The paper introduces a Lorentzian model and reports better-behaved geometry than in the Euclidean model (pp. 3, 10). But it describes a nontrivial continuum theory as a possibility, not a demonstrated numerical result (p. 10). Its two-sphere spatial topology is chosen for the model (p. 4); the paper does not report a continuum limit numerically matching a finite-sized spherical semiclassical configuration. (LLM, conf=0.88)
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Research works printed but not linked: 9
- [1][1] for recent reviews, see J. Ambjørn, J. Jurkiewicz and R. Loll: Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results, in: M-Theory and Quantum Geometry , eds. L. Thorlacius and T. Jonsson, NATO Science Series (Kluwer Academic Publishers, 2000) 382-449, hep-th/0001124; R. Loll: Discrete approaches to quantum gravity in four dimensions, Living Reviews in Relativity 13 (1998), http://www.livingreviews.org, gr-qc/9805049. - · arXiv
- [2][2] P. Bialas, Z. Burda, B. Petersson and J. Tabaczek: Appearance of mother universe and singular vertices in random geometries, Nucl. Phys. B 495 (1997) 463-476 [hep-lat/9608030]; P. Bialas, Z. Burda and D. Johnston: Condensation in the backgammon model, Nucl. Phys. B 493 (1997) 505-516. - · arXiv
- [3][3] J. Ambjorn, M. Carfora, D. Gabrielli and A. Marzuoli: Crumpled triangulations and critical points in 4D simplicial quantum gravity, Nucl. Phys. B 542 (1999) 349-394, hep-lat/9806035. - · arXiv
- [4][4] J. Ambjørn and R. Loll: Non-perturbative Lorentzian quantum gravity, causality and topology change, Nucl. Phys. B 536 (1998) 407-434, hep-th/9805108. - · arXiv
- [6][6] J. Ambjørn, K.N. Anagnostopoulos and R. Loll: Crossing the c=1 barrier in 2d Lorentzian quantum gravity, Phys. Rev. D 61 (2000) 044010, hep-lat/9909129. - · arXiv
- [7][7] J. Ambjørn, J. Jurkiewicz and R. Loll: Dynamically triangulating Lorentzian quantum gravity, preprint Golm AEI-2001-049. -
- [10][10] J. Ambjørn, M. Carfora and A. Marzuoli: The geometry of dynamical triangulations , Lecture Notes in Physics, New Series, m50, Springer, Berlin, 1997, hep-th/9612069. - · arXiv
- [11][11] I. Montvay and G. M¨ unster: Quantum fields on a lattice , Cambridge University Press, Cambridge, UK, 1994. -
- [12][12] D. Gabrielli: Polymeric phase of simplicial quantum gravity, Phys. Lett. B 421 (1998) 79-85, hep-lat/9710055. · arXiv
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- Authors
- Ambjørn, J., Jurkiewicz, J., & Loll, R.
- Affiliations
- Jagiellonian University (PL)
- Max Planck Society (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2000-07-31
- Volume
- 85
- Issue
- 5
- Pages
- 924-927
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2086412932
- Cited by
- 194
- References
- 0
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 8 · 2023: 9 · 2022: 5 · 2021: 9 · 2020: 4 · 2019: 8 · 2018: 1 · 2017: 10 · 2016: 6 · 2015: 8 · 2014: 10 · 2013: 13 · 2012: 17
- FWCI
- 6.45
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Max Planck Digital Library (submittedVersion, other-oa)
- Research at the University of Copenhagen (University of Copenhagen) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Lorentzian quantum gravity, Wick rotation, transfer matrix, Euclidean quantum gravity, lattice gravity
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