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This Causal Set Theory Bibliography is intended to aid causal set research. It gathers together academic papers, books, talks and PhD theses related to causal set theory and is intended to help readers find references which are often difficult to locate. Items are classified into sections based on their primary topic.

Introduction and Reviews

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  • J. Henson, The causal set approach to quantum gravity, arXiv:gr-qc/0601121; (Introduction, Overview)
  • R.D. Sorkin, Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School), In Proceedings of the Valdivia Summer School, edited by A. Gomberoff and D. Marolf; arXiv:gr-qc/0309009; (Introduction, Glossary)

Foundations

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  • R.D. Sorkin, Does a Discrete Order underly Spacetime and its Metric?, Proceedings of the Third Canadian Conference on General Relativity and Relativistic Astrophysics, (Victoria, Canada, May, 1989), edited by A. Coley, F. Cooperstock, B.Tupper, pp. 82-86, (World Scientific, 1990); (Introduction)
  • R.D. Sorkin, First Steps with Causal Sets, General Relativity and Gravitational Physics, (Proceedings of the Ninth Italian Conference of the same name, held Capri, Italy, September, 1990), 68-90, (World Scientific, Singapore), (1991), R. Cianci, R. de Ritis, M. Francaviglia, G. Marmo, C. Rubano, P. Scudellaro (eds.); (Introduction)
  • R.D. Sorkin, Spacetime and Causal Sets, Relativity and Gravitation: Classical and Quantum, (Proceedings of the SILARG VII Conference, held Cocoyoc, Mexico, December, 1990), pages 150-173, (World Scientific, Singapore, 1991), J.C. D’Olivo, E. Nahmad-Achar, M.Rosenbaum, M.P. Ryan, L.F. Urrutia and F. Zertuche (eds.); (Introduction)
  • R.D. Sorkin, Forks in the Road, on the Way to Quantum Gravity, Talk given at the conference entitled “Directions in General Relativity”, held at College Park, Maryland, May, 1993, Int. J. Th. Phys. 36: 2759–2781 (1997); arXiv:gr-qc/9706002; (Philosophical, Introduction)

Historical

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  • A. Einstein, Letter to H.S. Joachim, August 14, 1954; Item 13-453 cited in J. Stachel,“Einstein and the Quantum: Fifty Years of Struggle”, in From Quarks to Quasars,Philosophical Problems of Modern Physics, edited by R.G. Colodny (U. Pittsburgh Press, 1986), pages 380-381; (Historical)
  • G.'t Hooft, Quantum gravity: a fundamental problem and some radical ideas, Recent Developments in Gravitation (Proceedings of the 1978 Cargese Summer Institute) edited by M. Levy and S. Deser (Plenum, 1979); (Introduction, Foundations, Historical)
  • R.D. Sorkin, A Specimen of Theory Construction from Quantum Gravity, The Creation of Ideas in Physics: Studies for a Methodology of Theory Construction (Proceedings of the Thirteenth Annual Symposium in Philosophy, held Greensboro, North Carolina, March, 1989) pp. 167-179 (Number 55 in the University of Western Ontario Series in Philosophy of Science) (Kluwer Academic Publishers, Dordrecht, 1995) J. Leplin (ed.); arXiv:gr-qc/9511063; (Philosophical, Historical)

General

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  • H. Reichenbach; Axiomatik der relativistische Raum-Zeit-Lehre (translated into English as Axiomatization of the theory of relativity); Berkeley, University of California Press, 1969;;
  • D.D. Reid; Introduction to causal sets: an alternate view of spacetime structure; Canadian Journal of Physics 79, 1-16 (2001); arXiv:gr-qc/9909075; (General);

Manifoldness

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  • L. Bombelli, R.D. Sorkin, When are Two Lorentzian Metrics close?, General Relativity and Gravitation, proceedings of the 12th International Conference on General Relativity and Gravitation, held July 2-8, 1989, in Boulder, Colorado, USA, under the auspices of the International Society on General Relativity and Gravitation, 1989, p.220; (Closeness of Lorentzian manifolds)
  • L. Bombelli, Causal sets and the closeness of Lorentzian manifolds, Relativity in General: proceedings of the Relativity Meeting "93, held September 7-10, 1993, in Salas, Asturias, Spain. Edited by J. Diaz Alonso, M. Lorente Paramo. ISBN 2-86332-168-4. Published by Editions Frontieres, 91192 Gif-sur-Yvette Cedex, France, 1994, p. 249; (Closeness of Lorentzian manifolds)
  • L. Bombelli, Statistical Lorentzian geometry and the closeness of Lorentzian manifolds, J. Math. Phys.41:6944-6958 (2000); arXiv:gr-qc/0002053 (Closeness of Lorentzian manifolds, Manifoldness)
  • J. Henson, Constructing an interval of Minkowski space from a causal set, Class.Quant.Grav. 23 (2006) L29-L35; arXiv:gr-qc/0601069; (Continuum limit, Sprinkling)
  • S. Major, D.P. Rideout, S. Surya, On Recovering Continuum Topology from a Causal Set, J.Math.Phys.48:032501,2007; arXiv:gr-qc/0604124 (Continuum Topology)
  • S. Major, D.P. Rideout, S. Surya, Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory, arXiv:0902.0434 (Continuum topology and homology)
  • D.A. Meyer, The Dimension of Causal Sets I: Minkowski dimension, Syracuse University preprint (1988); (Dimension theory)
  • D.A. Meyer, The Dimension of Causal Sets II: Hausdorff dimension ,Syracuse University preprint (1988); (Dimension theory)
  • D.D. Reid, Manifold dimension of a causal set: Tests in conformally flat spacetimes, Phys.Rev. D67 (2003) 024034; arXiv:gr-qc/0207103v2 (Dimension theory)
  • R.D. Sorkin, Posets as Lattice Topologies, General Relativity and Gravitation, vol. I, 635-637 (Roma, Consiglio Nazionale Delle Ricerche, 1983), B. Bertotti, F. de Felice, A. Pascolini (eds.); (Topology)

Cosmological Constant

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  • Y. Jack Ng and H. van Dam, A small but nonzero cosmological constant; Int. J. Mod. Phys D. 10 : 49 (2001) arXiv:hep-th/9911102v3; (PreObservation Cosmological Constant)
  • Y. Kuznetsov, On cosmological constant in Causal Set theory; arXiv:0706.0041
  • R.D. Sorkin, A Modified Sum-Over-Histories for Gravity; reported in Highlights in gravitation and cosmology: Proceedings of the International Conference on Gravitation and Cosmology, Goa, India, 14-19 December, 1987, edited by B. R. Iyer, Ajit Kembhavi, Jayant V. Narlikar, and C. V. Vishveshwara, see pages 184-186 in the article by D. Brill and L. Smolin: “Workshop on quantum gravity and new directions”, pp 183-191 (Cambridge University Press, Cambridge, 1988); (PreObservation Cosmological Constant)
  • R.D. Sorkin, First Steps with Causal Sets, in R. Cianci, R. de Ritis, M. Francaviglia, G. Marmo, C. Rubano, P. Scudellaro (eds.), General Relativity and Gravitational Physics (Proceedings of the Ninth Italian Conference of the same name, held Capri, Italy, September, 1990), pp. 68-90 (World Scientific, Singapore, 1991); (PreObservation Cosmological Constant)
  • R.D. Sorkin; Forks in the Road, on the Way to Quantum Gravity, talk given at the conference entitled “Directions in General Relativity”, held at College Park, Maryland, May, 1993; Int. J. Th. Phys. 36 : 2759–2781 (1997) arXiv:gr-qc/9706002 ; (PreObservation Cosmological Constant)
  • R.D. Sorkin, Discrete Gravity; a series of lectures to the First Workshop on Mathematical Physics and Gravitation, held Oaxtepec, Mexico, Dec. 1995 (unpublished); (PreObservation Cosmological Constant)
  • R.D. Sorkin, Is the cosmological "constant" a nonlocal quantum residue of discreteness of the causal set type?; Proceedings of the PASCOS-07 Conference, July 2007, Imperial College London; arXiv:0710.1675; (Cosmological Constant)

Lorentz and Poincaré Invariance, Phenomenology

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  • F. Dowker, J. Henson, R.D. Sorkin, Quantum gravity phenomenology, Lorentz invariance and discreteness; Mod. Phys. Lett. A19, 1829–1840, (2004) arXiv:gr-qc/0311055v3; (Lorentz invariance, Phenomenology, Swerves)
  • J. Henson, Macroscopic observables and Lorentz violation in discrete quantum gravity; arXiv:gr-qc/0604040v1; (Lorentz invariance, Phenomenology)
  • N. Kaloper, D. Mattingly, Low energy bounds on Poincaré violation in causal set theory; Phys. Rev. D 74, 106001 (2006) arXiv:astro-ph/0607485 (Poincaré invariance, Phenomenology)
  • D. Mattingly, Causal sets and conservation laws in tests of Lorentz symmetry; Phys. Rev. D 77, 125021 (2008) arXiv:0709.0539 (Lorentz invariance, Phenomenology)

Black Hole Entropy

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  • D. Dou, Causal Sets, a Possible Interpretation for the Black Hole Entropy, and Related Topics; PhD thesis (SISSA, Trieste, 1999); arXiv:gr-qc/0106024 (Black hole entropy)
  • D. Dou, Black Hole Entropy as Causal Links; Fnd. of Phys, 33 2:279-296(18) (2003); arXiv:gr-qc/0302009v1 (Black hole entropy)
  • D.P. Rideout, S. Zohren, Counting entropy in causal set quantum gravity ; arXiv:gr-qc/0612074v1; (Black hole entropy)
  • D.P. Rideout, S. Zohren, Evidence for an entropy bound from fundamentally discrete gravity; Class.Quant.Grav. 23 (2006) 6195-6213; arXiv:gr-qc/0606065v2 (Black hole entropy)
  • R.D. Sorkin, On the Entropy of the Vacuum Outside a Horizon; Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. II, pp. 734-736 (Roma, Consiglio Nazionale Delle Ricerche, 1983), B. Bertotti, F. de Felice and A. Pascolini (eds.); (Black hole entropy)

Quantum Measure

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  • R.B. Salgado; Some Identities for the Quantum Measure and its Generalizations; arXiv:gr-qc/9903015; (Quantum Measure Theory)
  • R.D. Sorkin; Quantum measure theory and its interpretation; 4TH Drexel Symposium on Quantum Nonintegrability, 8-11 Sep 1994, Philadelphia, PA; arXiv:gr-qc/9507057; (Quantum Measure Theory)

Locality and Quantum Field Theory

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  • A.R. Daughton; The Recovery of Locality for Causal Sets and Related Topics; PhD thesis (Syracuse University, 1993); (Locality)
  • B.Z. Foster, T. Jacobson; Quantum field theory on a growing lattice; JHEP08(2004)024 arXiv:hep-th/0310166 (Quantum field theory)
  • S. Johnston; Particle propagators on discrete spacetime; 2008 Class. Quantum Grav. 25 202001; arXiv:0806.3083 (Quantum Field Theory)
  • R.D. Sorkin; Does Locality Fail at Intermediate Length-Scales; Towards Quantum Gravity, Daniele Oriti (ed.) (Cambridge University Press, 2007); arXiv:gr-qc/0703099v1; (d'Alembertian, Locality)
  • R. Sverdlov, L. Bombelli; Gravity and Matter in Causal Set Theory; arXiv:0801.0240

Dynamics

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  • A.Ash, P. McDonald, Moment Problems and the Causal Set Approach to Quantum Gravity; J.Math.Phys. 44 (2003) 1666-1678; arXiv:gr-qc/0209020
  • G. Brightwell, H.F. Dowker, R.S. Garcia, J. Henson, R.D. Sorkin; General covariance and the "problem of time" in a discrete cosmology; In ed. K. Bowden, Correlations:Proceedings of the ANPA 23 conference, August 16-21, 2001, Cambridge, England, pp. 1-17. Alternative Natural Philosophy Association, (2002).;arXiv:gr-qc/0202097; (Cosmology, Dynamics, Observables)
  • G. Brightwell, J. Henson, S. Surya; A 2D model of Causal Set Quantum Gravity: The emergence of the continuum; arXiv:0706.0375; (Quantum Dynamics, Toy Model)
  • A. Criscuolo, H. Waelbroeck; Causal Set Dynamics: A Toy Model; Class. Quant. Grav.16:1817-1832 (1999); arXiv:gr-qc/9811088; (Quantum Dynamics, Toy Model)
  • F. Dowker, S. Surya; Observables in extended percolation models of causal set cosmology;Class. Quant. Grav. 23, 1381-1390 (2006); arXiv:gr-qc/0504069v1; (Cosmology, Dynamics, Observables)
  • M. Droste, Universal homogeneous causal sets, J. Math. Phys. 46, 122503 (2005); arXiv:gr-qc/0510118; (Past-finite causal sets)
  • J. Henson; Comparing causality principles; Stud.Hist.Philos.Mod.Phys. 36 (2005) 519-543; arXiv:quant-ph/0410051v3; (Quantum Dynamics, Philosophy)
  • S. Major, D.P. Rideout, S. Surya; Spatial Hypersurfaces in Causal Set Cosmology; Class.Quant.Grav. 23 (2006) 4743-4752; arXiv:gr-qc/0506133v2; (Observables, Continuum topology)
  • A. Mallios, I. Raptis; Finitary Spacetime Sheaves of Quantum Causal Sets: Curving Quantum Causality arXiv:gr-qc/0102097
  • X. Martin, D. O'Connor, D.P. Rideout, R.D. Sorkin; On the “renormalization” transformations induced by cycles of expansion and contraction in causal set cosmology; Phys. Rev. D 63, 084026 (2001); arXiv:gr-qc/0009063 (Cosmology, Dynamics)
  • D.A. Meyer; Spacetime Ising models; (UCSD preprint May 1993); (Quantum Dynamics)
  • D.A. Meyer; Why do clocks tick?; General Relativity and Gravitation 25 9:893-900;; (Quantum Dynamics)
  • D.A. Meyer; Talk given at the 1997 Santa Fe workshop: Causal Sets and Feynman diagrams; Presented at "New Directions in Simplicial Quantum Gravity" July 28 - August 8, 1997; (Feynman diagrams, Quantum Dynamics)
  • I. Raptis; Algebraic Quantization of Causal Sets; Int.J.Theor.Phys 39:1233-1240,2000; arXiv:gr-qc/9906103; (Algebraic quantization);
  • D.P. Rideout, R.D. Sorkin; A classical sequential growth dynamics for causal sets, Phys. Rev D, 6, 024002 (2000);arXiv:gr-qc/9904062 (Cosmology, Dynamics)
  • R.D. Sorkin; Relativity theory does not imply that the future already exists: a counterexample; Relativity and the Dimensionality of the World, Vesselin Petkov (ed.) (Springer 2007, in press); arXiv:gr-qc/0703098v1; (Dynamics, Philosophy)
  • M. Varadarajan, D.P. Rideout; A general solution for classical sequential growth dynamics of Causal Sets; Phys.Rev. D73 (2006) 104021; arXiv:gr-qc/0504066v3; (Cosmology, Dynamics)

Geometry

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  • E. Bachmat; Discrete spacetime and its applications; arXiv:gr-qc/0702140; (Geodesics, Antichains)
  • S. He, D.P. Rideout; A Causal Set Black Hole; arXiv:0811.4235 (Causal structure of Schwarzschild spacetime, Sprinklings)
  • A.V. Levichev; Prescribing the conformal geometry of a lorentz manifold by means of its causal structure; Soviet Math. Dokl. 35:452-455, (1987); (Geometry, Causal Structure)
  • D.P. Rideout, P. Wallden; Spacelike distance from discrete causal order; arXiv:0810.1768 (Spatial distances)

Order Theory

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  • B. Bollobas, G. Brightwell; The dimension of random graph orders; The Mathematics of Paul Erdos II, R.L. Graham and J. Nesetril, eds. (Springer-Verlag, 1996), pp. 51-69; (Random partial orders);
  • B. Bollobas, G. Brightwell; The width of random graph orders; Math. Scientist 20: 69-90 (1995); (Random partial orders);
  • G. Brightwell; Models of Random Partial Orders; Surveys in Combinatorics, 1993, London Math. Soc. Lecture Notes Series 187:53-83, ed. Keith;; (Random partial orders);
  • G. Brightwell; M. Luczak; Order-invariant Measures on Causal Sets; arXiv:0901.0240; (Measures on causal sets)
  • G. Brightwell; M. Luczak; Order-invariant Measures on Fixed Causal Sets; arXiv:0901.0242; (Measures on causal sets)
  • G. Brightwell, P. Winkler; Sphere Orders; Order 6:235-240 (1989); (Order Theory);
  • D. Dhar; On phase transitions in posets; Pacific J. Math. 90: 299-305 (1980); (Phase Transitions for Posets, Order Theory);