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Dynamically triangulating Lorentzian quantum gravity

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Ambjørn, J., Jurkiewicz, J., Loll, R.·2001·Nuclear Physics B
DOI 10.1016/s0550-3213(01)00297-8
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Abstract

Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d < 4, with promising results. It is based on a simplicial regularization of Lorentzian space-times and, most importantly, possesses a well-defined, non-perturbative Wick rotation. We present a detailed analysis of the geometric and mathematical properties of the discretized model in d = 3,4. This includes a derivation of Lorentzian simplicial manifold constraints, the gravitational actions and their Wick rotation. We define a transfer matrix for the system and show that it leads to a well-defined self-adjoint Hamiltonian. In view of numerical simulations, we also suggest sets of Lorentzian Monte Carlo moves. We demonstrate that certain pathological phases found previously in Euclidean models of dynamical triangulations cannot be realized in the Lorentzian case.

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Research works printed but not linked: 40

  1. Williams, 1997, Recent progress in Regge calculus, Nucl. Phys. B (Proc. Suppl.), 57, 73, 10.1016/S0920-5632(97)00355-1 · DOI
  2. Ambjørn, 1995, Quantum gravity represented as dynamical triangulations, Class. Quant. Grav., 12, 2079, 10.1088/0264-9381/12/9/002 · DOI
  3. Loll, 1998, Discrete approaches to quantum gravity in four dimensions, Living Reviews in Relativity, 13
  4. Ambjørn, 1998, Non-perturbative Lorentzian quantum gravity, causality and topology change, Nucl. Phys. B, 536, 407, 10.1016/S0550-3213(98)00692-0 · DOI · Paper page
  5. Ambjørn, 1999, Euclidean and Lorentzian quantum gravity — lessons from two dimensions, J. Chaos Solitons Fractals, 10, 177, 10.1016/S0960-0779(98)00197-0 · DOI
  6. Loll, 2001, Discrete Lorentzian quantum gravity, Nucl. Phys. B (Proc. Suppl.), 94, 96, 10.1016/S0920-5632(01)00957-4 · DOI
  7. Krzywicki, 2000, Random manifolds and quantum gravity, Nucl. Phys. B (Proc. Suppl.), 83, 126, 10.1016/S0920-5632(00)91604-9 · doi:10.1016/s0920-5632(00)91604-9
  8. Thorleifsson, 1999, Lattice gravity and random surfaces, Nucl. Phys. B (Proc. Suppl.), 73, 133, 10.1016/S0920-5632(99)85013-0 · DOI
  9. Bowick, 1998, Random surfaces and lattice gravity, Nucl. Phys. B (Proc. Suppl.), 63, 77, 10.1016/S0920-5632(97)00699-3 · DOI
  10. Johnston, 1997, Gravity and random surfaces on the lattice: a review, Nucl. Phys. B (Proc. Suppl.), 53, 43, 10.1016/S0920-5632(96)00598-1 · DOI
  11. Caracciolo, 1988, Phases and topological structures of de Sitter lattice gravity, Nucl. Phys. B, 299, 693, 10.1016/0550-3213(88)90369-0 · DOI
  12. Beirl, 1994, The well defined phase of simplicial quantum gravity in four dimensions, Phys. Rev. D, 49, 5231, 10.1103/PhysRevD.49.5231 · DOI
  13. Beirl, 1997, Correlation functions in lattice formulation of quantum gravity, Nucl. Phys. B (Proc. Suppl.), 53, 735, 10.1016/S0920-5632(96)00768-2 · DOI
  14. Bialas, 1996, Focusing on the fixed point of 4-d simplicial gravity, Nucl. Phys. B, 472, 293, 10.1016/0550-3213(96)00214-3 · DOI
  15. de Bakker, 1996, Further evidence that the transition of 4-d dynamical triangulation is first order, Phys. Lett. B, 389, 238, 10.1016/S0370-2693(96)01277-4 · DOI
  16. Hamber, 2000, On the gravitational scaling dimensions, Phys. Rev. D, 61, 124008, 10.1103/PhysRevD.61.124008 · DOI
  17. Ambjørn, 2000, Nonperturbative Lorentzian path integral for gravity, Phys. Rev. Lett., 85, 924, 10.1103/PhysRevLett.85.924 · DOI · Paper page
  18. Ambjørn, 1990, Multiloop correlators for two-dimensional quantum gravity, Phys. Lett. B, 251, 517, 10.1016/0370-2693(90)90790-D · DOI · Paper page
  19. Di Francesco, 2000, Integrable 2d Lorentzian gravity and random walks, Nucl. Phys. B, 567, 515, 10.1016/S0550-3213(99)00661-6 · doi:10.1016/s0550-3213(99)00661-6
  20. Hartle, 1985, Simplicial minisuperspace I. General discussion, J. Math. Phys., 26, 804, 10.1063/1.526571 · DOI
  21. Sorkin, 1975, Time-evolution in Regge calculus, Phys. Rev. D, 12, 385, 10.1103/PhysRevD.12.385 · DOI
  22. Sorkin, 1981, Phys. Rev. D, 23, 565, 10.1103/PhysRevD.23.565 · DOI
  23. Ambjørn, 1997, The geometry of dynamical triangulations, Lecture Notes in Phys. New Ser., Monogr., 50
  24. Ambjørn, 1992, Three-dimensional simplicial quantum gravity, Nucl. Phys. B, 373, 557, 10.1016/0550-3213(92)90444-G · DOI
  25. Nakayama, 1994, 2-d quantum gravity in the proper time gauge, Phys. Lett. B, 325, 347, 10.1016/0370-2693(94)90023-X · DOI
  26. Osterwalder, 1973, Axioms for Euclidean Green's functions I, Commun. Math. Phys., 31, 83, 10.1007/BF01645738 · DOI · Paper page
  27. Osterwalder, 1975, Axioms for Euclidean Green's functions II, Commun. Math. Phys., 42, 281, 10.1007/BF01608978 · DOI · Paper page
  28. Seiler, 1982, Gauge theories as a problem of constructive quantum field theory and statistical mechanics, Lecture Notes in Phys., 159
  29. Gross, 1992, Elementary moves and ergodicity in d-dimensional simplicial quantum gravity, Nucl. Phys. B, 378, 367, 10.1016/0550-3213(92)90012-Z · DOI
  30. Ambjørn, 2001, Computer simulations of 3d Lorentzian quantum gravity, Nucl. Phys. B (Proc. Suppl.), 94, 689, 10.1016/S0920-5632(01)00878-7 · DOI · Paper page
  31. Gabrielli, 1998, Polymeric phase of simplicial quantum gravity, Phys. Lett. B, 421, 79, 10.1016/S0370-2693(98)00022-7 · DOI
  32. Ambjørn, 1999, Crumpled triangulations and critical points in 4D simplicial quantum gravity, Nucl. Phys. B, 542, 349, 10.1016/S0550-3213(98)00830-X · DOI
  33. Hotta, 1995, Singular vertices in the strong coupling phase of four-dimensional simplicial gravity, Prog. Theor. Phys., 94, 263, 10.1143/PTP.94.263 · DOI
  34. Hotta, 1996, Nucl. Phys. B (Proc. Suppl.), 47, 609, 10.1016/0920-5632(96)00132-6 · DOI
  35. Catterall, 1996, Singular vertices and the triangulation space of the d sphere, Nucl. Phys. B, 468, 263, 10.1016/0550-3213(96)00130-7 · DOI
  36. Catterall, 1998, Singular structure in 4-d simplicial gravity, Phys. Lett. B, 416, 274, 10.1016/S0370-2693(97)01349-X · DOI
  37. Ambjørn, 2000, The relation between Euclidean and Lorentzian 2D quantum gravity, Phys. Lett. B, 475, 24, 10.1016/S0370-2693(00)00058-7 · DOI
  38. Ambjørn, 1999, A new perspective on matter coupling in 2d quantum gravity, Phys. Rev. D, 60, 104035, 10.1103/PhysRevD.60.104035 · DOI
  39. Ambjørn, 2000, Crossing the c=1 barrier in 2d Lorentzian quantum gravity, Phys. Rev. D, 61, 044010, 10.1103/PhysRevD.61.044010 · DOI
  40. Dasgupta, 2001, A proper-time cure for the conformal sickness in quantum gravity, Nucl. Phys. B, 606, 357, 10.1016/S0550-3213(01)00227-9 · DOI · Paper page

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Metadata

Authors
Ambjørn, J., Jurkiewicz, J., & Loll, R.
Venue
Nuclear Physics B
Publisher
Elsevier BV
Published
2001-09
Volume
610
Issue
1-2
Pages
347-382
ISSN
0550-3213 (ISSN-L)
DOI
10.1016/s0550-3213(01)00297-8
OpenAlex
W2116483569
Cited by
312
References
2
FWCI
6.50
Type
journal article
Language
en
Open access
green
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)

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CoChat. (2026). Citation check: Dynamically triangulating Lorentzian quantum gravity. https://app.cochat.ai/papers/10.1016/s0550-3213(01)00297-8
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Ambjørn, J., Jurkiewicz, J., & Loll, R. (2001). Dynamically triangulating Lorentzian quantum gravity. Nuclear Physics B. https://doi.org/10.1016/s0550-3213(01)00297-8

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