Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)

These are lecture notes on causal set theory prepared in Jan. 2002 for a Summer School in Valdivia, Chile. In some places, they are more complete, in others much less so, regrettably. An extensive set of references and a glossary of terms can be found at the end of the notes.

[1]  R. Sorkin,et al.  Evidence for a continuum limit in causal set dynamics , 2000, gr-qc/0003117.

[2]  Moment problems and the causal set approach to quantum gravity , 2002, gr-qc/0209020.

[3]  R. Sorkin,et al.  Classical sequential growth dynamics for causal sets , 1999, gr-qc/9904062.

[4]  Charles M. Newman,et al.  Chain Lengths in Certain Random Directed Graphs , 1992, Random Struct. Algorithms.

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[11]  A Specimen of Theory Construction from Quantum Gravity , 1995, gr-qc/9511063.

[12]  Statistical Lorentzian geometry and the closeness of Lorentzian manifolds , 2000, gr-qc/0002053.

[13]  Boris G. Pittel,et al.  A phase transition phenomenon in a random directed acyclic graph , 2001, Random Struct. Algorithms.

[14]  Andrew King,et al.  A new topology for curved space–time which incorporates the causal, differential, and conformal structures , 1976 .

[15]  R. Sorkin,et al.  Spacetime as a Causal Set , 1989 .

[16]  L. Smolin.  The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology , 1994, gr-qc/9404011.

[17]  Black Hole Entropy and Induced Gravity , 1994, gr-qc/9404039.

[18]  Some Identities for the Quantum Measure and its Generalizations , 1999, gr-qc/9903015.

[19]  A. Daughton.  An investigation of the symmetric case of when causal sets can embed into manifolds , 1998 .

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[21]  Rafael D. Sorkin,et al.  General Covariance and the "Problem of Time" in a Discrete Cosmology , 2002 .

[22]  A. Hosoya.  Topology Change in Quantum Gravity , 1993 .

[23]  D. Malament.  The class of continuous timelike curves determines the topology of spacetime , 1977 .

[24]  A. Daughton.  The recovery of locality for causal sets and related topics , 1993 .

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[27]  A new topology on the space of Lorentzian metrics on a fixed manifold , 2002, 1104.1811.

[28]  R. Sorkin.  On the Entropy of the Vacuum Outside a Horizon , 2014, 1402.3589.

[29]  R. Sorkin.  Quantum mechanics as quantum measure theory , 1994, gr-qc/9401003.

[30]  Rafael D. Sorkin.  Indications of Causal Set Cosmology , 1998 .

[31]  Rafael D. Sorkin.  Forks in the road, on the way to quantum gravity , 1997 .

[32]  Gregory,et al.  Structure of random discrete spacetime. , 1990, Physical review letters.

[33]  R. Sorkin,et al.  “Renormalization” transformations induced by cycles of expansion and contraction in causal set cosmology , 2000, gr-qc/0009063.

[34]  Boris G. Pittel,et al.  On Tail Distribution of Interpost Distance , 2000, J. Comb. Theory, Ser. B.

[35]  M. Taketani.  On Formation of the Newton Mechanics , 1971 .

[36]  V. Kazakov.  The Appearance of Matter Fields from Quantum Fluctuations of 2D Gravity , 1989 .

[37]  D. Meyer.  Spherical containment and the Minkowski dimension of partial orders , 1993 .

[38]  Jacobson,et al.  Black-hole evaporation and ultrashort distances. , 1991, Physical review. D, Particles and fields.

[39]  Causal evolution of spin networks , 1997, gr-qc/9702025.

[40]  Mohamed H. El-Zahar,et al.  On sphere orders , 1998, Discret. Math..

[41]  David Rideout.  Dynamics of causal sets , 2001 .

[42]  J. Lense.  Über die Hypothesen, welche der Geometrie zu Grunde liegen , 1922 .

[43]  E. Witten.  Quantum Gravity In De Sitter Space , 2001, hep-th/0106109.

[44]  David A. Meyer,et al.  The origin of Lorentzian geometry , 1989 .

[45]  Klaus Simon,et al.  On the Distribution of the Transitive Closure in a Random Acyclic Digraph , 1993, ESA.

[46]  CAUSAL SET DYNAMICS: A TOY MODEL , 1998, gr-qc/9811088.

[47]  Rafael D. Sorkin,et al.  ``Observables'' in causal set cosmology , 2003 .

[48]  Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime , 1993, gr-qc/9304006.

[49]  P. Panangaden,et al.  Discrete Quantum Causal Dynamics , 2001, International Journal of Theoretical Physics.

[50]  Causal Sets, a Possible Interpretation for the Black Hole Entropy,and Related Topics , 2001, gr-qc/0106024.

[51]  D. D. Reid.  Discrete quantum gravity and causal sets , 2001 .

[52]  E. Zeeman.  Causality Implies the Lorentz Group , 1964 .

[53]  G. Brightwell.  Models of random partial orders , 1993 .