cdt-newtonian-limit-biblio.bib

@techreport{ambjorn_geometry_1996,
	type = {{arXiv} e-print},
	title = {The geometry of dynamical triangulations},
	note = {\url{http://arxiv.org/abs/hep-th/9612069}},
	abstract = {We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the {MonteCarlo} simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.},
	number = {hep-th/9612069},
	urldate = {2013-09-27},
	author = {Ambjorn, J. and Carfora, M. and Marzuoli, A.},
	month = dec,
	year = {1996},
	note = {{Lect.NotesPhys.50:197},1997},
	keywords = {Causal Dynamical Triangulations, General Relativity and Quantum Cosmology, High Energy Physics - Lattice, High Energy Physics - Theory},
	annote = {Comment: 166 pages, Revtex (latex) file},
	file = {arXiv.org Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/IPC65CPX/9612069.html:text/html;hep-th/9612069 PDF:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/U35IF6KI/Ambjorn et al. - 1996 - The geometry of dynamical triangulations.pdf:application/pdf}
}
@article{cdt,
	title = {A non-perturbative {L}orentzian path integral for gravity},
	volume = {85},
	lccn = {0000},
	note = {\url{http://arxiv.org/abs/hep-th/0002050}},
	abstract = {A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time. For finite lattice volume, the associated transfer matrix is self-adjoint and bounded. The reflection positivity of the model ensures the existence of a well-defined Hamiltonian. The degenerate geometric phases found previously in dynamically triangulated Euclidean gravity are not present. The phase structure of the new Lorentzian quantum gravity model can be readily investigated by both analytic and numerical methods.},
	urldate = {2008-05-05},
	journal = {Physical Review Letters},
	author = {{J. Ambjorn} and {J. Jurkiewicz} and {R. Loll}},
	month = feb,
	year = {2000},
	note = {{Phys.Rev.Lett.} 85 (2000)},
	keywords = {Causal Dynamical Triangulations, quantum gravity, Read},
	pages = {924--7},
	file = {0002050v3.pdf:files/381/0002050v3.pdf:application/pdf}
}

@article{rovelli_notes_2000,
	title = {Notes for a brief history of quantum gravity},
	lccn = {0104},
	note = {\url{http://arxiv.org/abs/gr-qc/0006061}},
	abstract = {I sketch the main lines of development of the research in quantum gravity, from the first explorations in the early thirties to nowadays.},
	urldate = {2011-03-11},
	journal = {gr-qc/0006061},
	author = {Rovelli, Carlo},
	month = jun,
	year = {2000},
	keywords = {General Relativity and Quantum Cosmology, High Energy Physics - Theory},
	file = {arXiv.org Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/5UJDHQ52/0006061.html:text/html;gr-qc/0006061 PDF:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/32WNE2JJ/Rovelli - 2000 - Notes for a brief history of quantum gravity.pdf:application/pdf}
}

@article{kommu_validation_2011,
	title = {A {V}alidation of {C}ausal {D}ynamical {T}riangulations},
	note = {\url{http://arxiv.org/abs/1110.6875}},
	abstract = {The Causal Dynamical Triangulation ({CDT)} approach to quantum gravity is a lattice approximation to the gravitational path integral. Developed by Ambj{\textbackslash}o\{\}rn, Jurkiewicz and Loll, it has yielded some important results, notably the emergence of classical spacetime and short scale dimensional reduction. However, virtually all the results reported so far have been based on a single computer code. In this paper we present the first completely independent verification of the {CDT} algorithm, and report the successful reproduction of the emergence of classical spacetime and smooth reduction in the spectral dimension of the 2+1 and 3+1 dimensional spacetimes.},
	urldate = {2012-11-10},
	journal = {{arXiv:1110.6875}},
	author = {Kommu, Rajesh},
	month = oct,
	year = {2011},
	keywords = {General Relativity and Quantum Cosmology, High Energy Physics - Theory},
	file = {1110.6875 PDF:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/6UPTQD3T/Kommu - 2011 - A Validation of Causal Dynamical Triangulations.pdf:application/pdf;arXiv.org Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/MJFZF93S/1110.html:text/html}
}

@article{ambjorn_semiclassical,
	title = {Semiclassical {U}niverse from {F}irst {P}rinciples},
	volume = {607},
	lccn = {0059},
	note = {\url{http://arxiv.org/abs/hep-th/0411152}},
	abstract = {Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in the Euclidean sector of this theory is a bounce which satisfies a semiclassical equation. After integrating out all degrees of freedom except for a global scale factor, we obtain the ground state wave function of the universe as a function of this scale factor.},
	number = {2005},
	urldate = {2009-03-16},
	journal = {Physics Letters B},
	author = {{J. Ambjorn} and {J. Jurkiewicz} and {R. Loll}},
	keywords = {Causal Dynamical Triangulations, Read},
	pages = {205--213},
	annote = {Read 6th},
	file = {[hep-th/0411152] Semiclassical Universe from First Principles:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/TC2AM4T6/0411152.html:text/html;0411152v1.pdf:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/IXTTMJU5/0411152v1.pdf:application/pdf}
}

@book{synge_relativity,
	title = {Relativity: the general theory},
	shorttitle = {Relativity},
	publisher = {{North-Holland} Pub. Co.},
	author = {Synge, John Lighton},
	year = {1960},
	keywords = {General relativity {(Physics)}, Relativity {(Physics)}, Science / Relativity}
}

@article{curzon_cylindrical_1925,
	title = {Cylindrical {S}olutions of {E}instein's {G}ravitation {E}quations},
	volume = {s2-23},
	journal = {Proceedings of the London Mathematical Society},
	issn = {0024-6115, 1460-{244X}},
	url = {http://plms.oxfordjournals.org/content/s2-23/1/477.full.pdf+html?frame=sidebar},
	doi = {10.1112/plms/s2-23.1.477},
	number = {1},
	urldate = {2013-10-16},
	author = {Curzon, H. E. J.},
	month = jan,
	year = {1925},
	pages = {477--480},
	file = {Curzon - 1925 - Cylindrical Solutions of Einstein's Gravitation Eq.pdf:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/F52HS87Q/Curzon - 1925 - Cylindrical Solutions of Einstein's Gravitation Eq.pdf:application/pdf;Cylindrical Solutions of Einstein's Gravitation Equations:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/M9X84IJ2/477.full.html:text/html}
	}

@article{curzon1924,
	title = {Cylindrical {S}olutions of {E}instein's {G}ravitational {E}quations},
	volume = {s2--23},
	journal = {Proceedings of the London Mathematical Society},
	author = {Curzon, H. E. J.},
	year = {1925},
	pages = {477--480}
}

@article{einstein-rosen-1936,
  title = {Two-{B}ody {P}roblem in {G}eneral {R}elativity {T}heory},
  author = {Einstein, A. and Rosen, N.},
  journal = {Phys. Rev.},
  volume = {49},
  issue = {5},
  pages = {404--405},
  year = {1936},
  month = {Mar},
  doi = {10.1103/PhysRev.49.404.2},
  note = {\url{http://link.aps.org/doi/10.1103/PhysRev.49.404.2}},
  publisher = {American Physical Society}
}

@article{katz1967derivation,
	title = {Derivation of {N}ewton's {L}aw of {G}ravitation from {G}eneral {R}elativity},
	volume = {9},
	lccn = {0000},
	abstract = {A static situation of two objects held apart by a strut is considered within the framework of general relativity, and the gravitational attraction between the objects is inferred from the stress in the strut. In the Newtonian limit -- the objects are well separated and the field weak everywhere except in their immediate vicinity -- Newton's law of gravitation is reproduced. This check goes well beyond verifications of the Newtonian limit based on considerations of "test particles", since arbitrarily strong self-fields are not excluded for either object. It is also an explicit verification of the equality of active and passive gravitational masses.},
	number = {7},
	journal = {Journal of Mathematical Physics},
	author = {Katz, Amnon},
	month = sep,
	year = {1967},
	pages = {983--985}
}

@article{ambjorn_semiclassical_2011,
	title = {The {S}emiclassical {L}imit of {C}ausal {D}ynamical {T}riangulations},
	lccn = {0000},
	note = {\url{http://arxiv.org/abs/1102.3929}},
	abstract = {Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations ({CDT)} is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature of this semiclassical limit we present a detailed study of the three-volume data, which allows us to re-confirm the de Sitter structure, exhibit short-distance discretization effects, and make a first detailed investigation of the presence of higher-order curvature terms in the effective action for the scale factor. Technically, we make use of a novel way of fixing the total four-volume in the simulations.},
	urldate = {2011-03-11},
	journal = {1102.3929},
	author = {Ambjorn, J. and Gorlich, A. and Jurkiewicz, J. and Loll, R. and Gizbert-Studnicki, J. and Trzesniewski, T.},
	month = feb,
	year = {2011},
	keywords = {General Relativity and Quantum Cosmology, High Energy Physics - Lattice, High Energy Physics - Theory},
	annote = {Read 8th},
	file = {1102.3929 PDF:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/ACAD59PF/Ambjorn et al. - 2011 - The Semiclassical Limit of Causal Dynamical Triang.pdf:application/pdf;arXiv.org Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/2C6256CT/1102.html:text/html}
}


@article{letelier_superposition_1997,
	title = {Superposition of {W}eyl solutions: The equilibrium forces},
	shorttitle = {Superposition of Weyl solutions},
	note = {\url{http://arxiv.org/abs/gr-qc/9710122}},
	doi = {10.1088/0264-9381/15/2/015},
	abstract = {Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detail},
	urldate = {2011-10-12},
	journal = {{arXiv:gr-qc/9710122}},
	author = {Letelier, Patricio. S and Oliveira, Samuel R},
	month = oct,
	year = {1997},
	note = {{Class.Quant.Grav.} 15 (1998) 421-433},
	keywords = {General Relativity and Quantum Cosmology},
	file = {arXiv.org Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/MRZIZQTF/9710122.html:text/html;gr-qc/9710122 PDF:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/R7QG93EB/Letelier and Oliveira - 1997 - Superposition of Weyl solutions The equilibrium f.pdf:application/pdf}
}

% Optional fields: author, title, howpublished, month, year, note
@MISC{cgal,
	title = "\textsc{Cgal}, {C}omputational {G}eometry {A}lgorithms {L}ibrary",
    note  = {\url{http://www.cgal.org}}	
}
% Optional fields: volume, number, pages, month, note
@ARTICLE{regge,
	author = {Regge, T},
	title = {General {R}elativity without {C}oordinates},
	journal = {Nuovo Cimento A},
	year = {1961},
	volume = {19},
	pages = {558--571}
}
@article{barrett_1986,
	title = {The {E}instein tensor in {R}egge's discrete gravity theory},
	volume = {3},
	issn = {0264-9381},
	note = {\url{http://iopscience.iop.org/0264-9381/3/2/014}},
	doi = {10.1088/0264-9381/3/2/014},
	abstract = {The relation between Regge's equations of motion for a simplicial manifold and the distributional Einstein tensor of the manifold is discussed. Regge's equations imply that the distributional Einstein tensor vanishes 'on average', the averaging involving integrating contributions to the Einstein tensor on a suitably defined 3-surface.},
	language = {en},
	number = {2},
	urldate = {2013-09-02},
	journal = {Classical and Quantum Gravity},
	author = {Barrett, J. W.},
	month = mar,
	year = {1986},
	pages = {203},
	file = {Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/5722E8TQ/014.html:text/html;The Einstein tensor in Regge's discrete gravity theory.pdf:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/7G7KQSGV/The Einstein tensor in Regge's discrete gravity theory.pdf:application/pdf}
}
@BOOK{cgal:eb-12b,
   PUBLISHER    = {{CGAL Editorial Board}},
   TITLE        = {{CGAL} User and Reference Manual},
   YEAR         = {2013},
   AUTHOR       = {{The CGAL Project}},
   ALTEDITOR    = {},
   EDITION      = {{4.2}},
   NOTE      	= {\url{http://www.cgal.org/Manual/4.2/doc_html/cgal_manual/packages.html}},
}
@techreport{ambjorn_nonperturbative_2012,
	type = {{arXiv} e-print},
	title = {Nonperturbative Quantum Gravity},
	note = {\url{http://arxiv.org/abs/1203.3591}},
	abstract = {Asymptotic safety describes a scenario in which general relativity can be quantized as a conventional field theory, despite being nonrenormalizable when expanding it around a fixed background geometry. It is formulated in the framework of the Wilsonian renormalization group and relies crucially on the existence of an ultraviolet fixed point, for which evidence has been found using renormalization group equations in the continuum. {"Causal} Dynamical Triangulations" ({CDT)} is a concrete research program to obtain a nonperturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories. In the Wilsonian spirit one can use this formulation to try to locate fixed points of the lattice theory and thereby provide independent, nonperturbative evidence for the existence of a {UV} fixed point. We describe the formalism of {CDT}, its phase diagram, possible fixed points and the "quantum geometries" which emerge in the different phases. We also argue that the formalism may be able to describe a more general class of Ho{\textbackslash}v\{r\}ava-Lifshitz gravitational models.},
	number = {1203.3591},
	urldate = {2013-06-04},
	author = {Ambjorn, J. and Goerlich, A. and Jurkiewicz, J. and Loll, R.},
	month = mar,
	year = {2012},
	note = {Physics Reports 519, 2012, 127-210},
	keywords = {General Relativity and Quantum Cosmology, High Energy Physics - Lattice, High Energy Physics - Theory, Read},
	annote = {Comment: Review, 146 pages, many figures},
	file = {1203.3591 PDF:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/HSXEMDS9/Ambjorn et al. - 2012 - Nonperturbative Quantum Gravity.pdf:application/pdf;arXiv.org Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/62ETT5Z9/1203.html:text/html}
}

@article{david_simplicial_1993,
	title = {Simplicial Quantum Gravity and Random Lattices},
	url = {http://arxiv.org/abs/hep-th/9303127},
	abstract = {Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus - dynamical triangulations 3. Two dimensional quantum gravity, dynamical triangulations and matrix models continuum formulation - dynamical triangulations and continuum limit - one matrix model - various matrix models - numerical studies - c=1 barrier - intrinsic geometry of 2d gravity - Liouville at c{\textgreater}25 4. Euclidean quantum gravity in three and four dimensions what are we looking for? - 3d simplicial gravity - 4d simplicial gravity - 3d and 4d Regge calculus 5. Non-perturbative problems in two dimensional quantum gravity double scaling limit - string equation - non-perturbative properties of the string equation - divergent series and Borel summability - non-perturbative effects in 2d gravity and string theories - stabilization proposals 6. Conclusion},
	urldate = {2013-11-27},
	journal = {{arXiv:hep-th/9303127}},
	author = {David, F.},
	month = mar,
	year = {1993},
	keywords = {High Energy Physics - Theory},
	annote = {Comment: (Lectures given at Les Houches Summer School, July 1992) 63 pages, plain {TeX} (foreword) + uuencoded tar-compressed {PostScript} file (main text + figures)},
	annote = {Read 0},
	file = {arXiv.org Snapshot:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/4VRDCHUT/9303127.html:text/html;hep-th/9303127 PDF:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/E5R34SRP/David - 1993 - Simplicial Quantum Gravity and Random Lattices.pdf:application/pdf}

	@book{carroll_spacetime_2003,
	title = {Spacetime and Geometry: An Introduction to General Relativity},
	isbn = {0805387323},
	shorttitle = {Spacetime and Geometry},
	publisher = {Benjamin Cummings},
	author = {Carroll, Sean},
	month = sep,
	year = {2003}
}