---
title: "References and Citations"
description: "Academic references and bibliographic citations used throughout the causal-triangulations library"
keywords: ["references", "citations", "causal dynamical triangulations", "quantum gravity", "bibliography"]
author: "Adam Getchell"
date: "2025-10-07"
category: "Documentation"
tags: ["academic", "research", "citations", "physics", "quantum gravity"]
layout: "page"
---

## How to Cite This Library

If you use this library in your research or project, please cite it using the information provided in our [CITATION.cff](CITATION.cff) file. This file contains structured citation metadata that can be automatically processed by GitHub and other platforms.

**Quick citation:**

```text
Adam Getchell. 2025. causal-triangulations: A Causal Dynamical Triangulation library for quantum gravity research.
GitHub. https://github.com/acgetchell/causal-triangulations
```

For BibTeX, APA, or other citation formats, please refer to the [CITATION.cff](CITATION.cff) file or use GitHub's "Cite this repository" feature.

## Foundational Causal Dynamical Triangulations Theory

This section contains the seminal papers and foundational work that established CDT as a non-perturbative approach to quantum gravity.

### Original CDT Framework

- Ambjørn, J., Jurkiewicz, J., and Loll, R. "Dynamically Triangulating Lorentzian Quantum Gravity." _Nuclear Physics B_ 610, no. 1-2 (2001): 347-382. DOI: [10.1016/S0550-3213(01)00297-8](https://doi.org/10.1016/S0550-3213(01)00297-8). arXiv: [hep-th/0105267](https://arxiv.org/abs/hep-th/0105267)

- Ambjørn, J., Jurkiewicz, J., and Loll, R. "Emergence of a 4D World from Causal Quantum Gravity." _Physical Review Letters_ 93, no. 13 (2004): 131301. DOI: [10.1103/PhysRevLett.93.131301](https://doi.org/10.1103/PhysRevLett.93.131301). arXiv: [hep-th/0404156](https://arxiv.org/abs/hep-th/0404156)

### Comprehensive Reviews

- Loll, R. "Quantum Gravity from Causal Dynamical Triangulations: A Review." _Classical and Quantum Gravity_ 37, no. 1 (2020): 013002. DOI: [10.1088/1361-6382/ab57c7](https://doi.org/10.1088/1361-6382/ab57c7). arXiv: [1905.08669](https://arxiv.org/abs/1905.08669)

- Ambjørn, J., Görlich, A., Jurkiewicz, J., and Loll, R. "Nonperturbative Quantum Gravity." _Physics Reports_ 519, no. 4-5 (2012): 127-210. DOI: [10.1016/j.physrep.2012.03.007](https://doi.org/10.1016/j.physrep.2012.03.007). arXiv: [1203.3591](https://arxiv.org/abs/1203.3591)

## Monte Carlo Methods in Quantum Gravity

These references provide the algorithmic foundations for Monte Carlo simulations in discrete quantum gravity.

### Metropolis-Hastings Algorithm in CDT

- Ambjørn, J., and Loll, R. "Non-perturbative Lorentzian quantum gravity, causality and topology change." _Nuclear Physics B_ 536, no. 1-2 (1998): 407-434. DOI: [10.1016/S0550-3213(98)00692-0](https://doi.org/10.1016/S0550-3213(98)00692-0). arXiv: [hep-th/9805108](https://arxiv.org/abs/hep-th/9805108)

### Regge Calculus and Discrete Action

- Regge, T. "General Relativity without coordinates." _Il Nuovo Cimento_ 19, no. 3 (1961): 558-571. DOI: [10.1007/BF02733251](https://doi.org/10.1007/BF02733251)

- Hamber, H. W. "Quantum Gravitation: The Feynman Path Integral Approach." Berlin: Springer-Verlag, 2009. DOI: [10.1007/978-3-540-85293-3](https://doi.org/10.1007/978-3-540-85293-3)

### Ergodic Moves and Alexander Moves

- Alexander, J. W. "The combinatorial theory of complexes." _Annals of Mathematics_ 31, no. 2 (1930): 292-320. DOI: [10.2307/1968099](https://doi.org/10.2307/1968099)

- Pachner, U. "P.L. homeomorphic manifolds are equivalent by elementary shellings." _European Journal of Combinatorics_ 12, no. 2 (1991): 129-145. DOI: [10.1016/S0195-6698(13)80080-7](https://doi.org/10.1016/S0195-6698(13)80080-7)

## Computational Geometry and Delaunay Triangulations

This library leverages computational geometry for efficient triangulation operations.

### Delaunay Triangulation Algorithms

- Bowyer, A. "Computing Dirichlet tessellations." _The Computer Journal_ 24, no. 2 (1981): 162-166. DOI: [10.1093/comjnl/24.2.162](https://doi.org/10.1093/comjnl/24.2.162)

- Watson, D.F. "Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes." _The Computer Journal_ 24, no. 2 (1981): 167-172. DOI: [10.1093/comjnl/24.2.167](https://doi.org/10.1093/comjnl/24.2.167)

### Computational Geometry References

- de Berg, M., et al. "Computational Geometry: Algorithms and Applications." 3rd ed. Berlin: Springer-Verlag, 2008. DOI: [10.1007/978-3-540-77974-2](https://doi.org/10.1007/978-3-540-77974-2)

- The CGAL Project. "CGAL User and Reference Manual." CGAL Editorial Board, 6.0.1 edition, 2024. Available at: <https://doc.cgal.org/6.0.1/Manual/packages.html>

## Discrete Approaches to General Relativity

### Lattice Approaches to Quantum Gravity

- Williams, R. M., and Tuckey, P. A. "Regge calculus: a brief review and bibliography." _Classical and Quantum Gravity_ 9, no. 5 (1992): 1409. DOI: [10.1088/0264-9381/9/5/021](https://doi.org/10.1088/0264-9381/9/5/021)

- Sorkin, R. D. "Causal sets: discrete gravity." In _Lectures on Quantum Gravity_, edited by A. Gomberoff and D. Marolf, 305-327. Boston: Springer, 2005. arXiv: [gr-qc/0309009](https://arxiv.org/abs/gr-qc/0309009)

### Spin Foam Models and Loop Quantum Gravity

- Rovelli, C. "Quantum Gravity." Cambridge: Cambridge University Press, 2004. DOI: [10.1017/CBO9780511755804](https://doi.org/10.1017/CBO9780511755804)

- Perez, A. "The Spin Foam Approach to Quantum Gravity." _Living Reviews in Relativity_ 16, no. 1 (2013): 3. DOI: [10.12942/lrr-2013-3](https://doi.org/10.12942/lrr-2013-3). arXiv: [1205.2019](https://arxiv.org/abs/1205.2019)

## Numerical Methods and Performance

### High-Performance Scientific Computing

- Press, W. H., et al. "Numerical Recipes: The Art of Scientific Computing." 3rd ed. Cambridge: Cambridge University Press, 2007. ISBN: 978-0-521-88068-8

- Golub, G. H., and Van Loan, C. F. "Matrix Computations." 4th ed. Baltimore: Johns Hopkins University Press, 2013. ISBN: 978-1-4214-0794-4

### Formal Verification in Scientific Computing

- Boldo, S., and Melquiond, G. "Computer Arithmetic and Formal Proofs." London: ISTE Press, 2017. ISBN: 978-1-78548-254-3

- Muller, J.-M., et al. "Handbook of Floating-Point Arithmetic." 2nd ed. Basel: Birkhäuser, 2018. DOI: [10.1007/978-3-319-76526-6](https://doi.org/10.1007/978-3-319-76526-6)

## Related Software and Libraries

### Computational Geometry Libraries

- The CGAL Project. "CGAL: Computational Geometry Algorithms Library." <https://www.cgal.org/>

- Shewchuk, J. R. "Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator." In _Applied Computational Geometry Towards Geometric Engineering_, 203-222. Berlin: Springer, 1996. DOI: [10.1007/BFb0014497](https://doi.org/10.1007/BFb0014497)

### Monte Carlo and Statistical Physics

- Newman, M. E. J., and Barkema, G. T. "Monte Carlo Methods in Statistical Physics." Oxford: Oxford University Press, 1999. ISBN: 978-0-19-851797-9

- Landau, D. P., and Binder, K. "A Guide to Monte Carlo Simulations in Statistical Physics." 4th ed. Cambridge: Cambridge University Press, 2014. DOI: [10.1017/CBO9781139696463](https://doi.org/10.1017/CBO9781139696463)
