This repository contains some example functions and scripts that use my Python modules causets
.
The script file lightcone_animations.py
was used to create animations that can be found at the following YouTube links.
Simplices in de Sitter, Minkowski, and Schwarzschild spacetimes
![Lightcones of a causal 1-simplex embedded in 2-dimensional de Sitter spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/de Sitter 1-simplex.png) |
de Sitter spacetime, 1-simplex |
![Lightcones of a causal 2-simplex embedded in 3-dimensional de Sitter spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/de Sitter 2-simplex.png) |
de Sitter spacetime, 2-simplex |
![Lightcones of a causal 1-simplex embedded in 2-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 1-simplex.png) |
Minkowski spacetime, 1-simplex |
![Lightcones of a causal 2-simplex embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 2-simplex.png) |
Minkowski spacetime, 2-simplex |
![Lightcones of a causal 2-simplex with one edge flipped embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 2-simplex with one edge flipped.png) |
Minkowski spacetime, 2-simplex with one edge flipped |
![Lightcones of a causal 2-simplex with two edges flipped embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 2-simplex with two edges flipped.png) |
Minkowski spacetime, 2-simplex with two edges flipped |
![Lightcones of a causal 3-simplex embedded in 4-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3-simplex.png) |
Minkowski spacetime, 3-simplex |
![Lightcones of a causal 1-simplex embedded in 2-dimensional Schwarzschild spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Schwarzschild 1-simplex.png) |
Schwarzschild spacetime, 1-simplex |
Subsets of lattices in Minkowski spacetime
![Lightcones of a causal 2D-lattice embedded in 2-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 2D-lattice.png) |
Subset of a 2D-lattice |
![Lightcones of a causal 3D-lattice of octahedrons embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice of octahedrons.png) |
Subset of a 3D-lattice (octahedrons) |
![Lightcones of a causal 4D-lattice of octahedrons embedded in 4-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 4D-lattice of octahedrons.png) |
Subset of a 4D-lattice (octahedrons) |
![Lightcones of a causal 3D-lattice of octahedrons embedded in 3-dimensional Minkowski spacetime (smaller subset)](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice of octahedrons (small).png) |
Smaller subset of a 3D-lattice (octahedrons) |
![Lightcones of a causal 3D-lattice in FCC embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice in FCC.png) |
Subset of a 3D-lattice (FCC) |
![Lightcones of a causal 3D-lattice in HCP embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice in HCP.png) |
Subset of a 3D-lattice (HCP) |
![Lightcones of a causal 3D-lattice of rhombohedrons embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice of rhombohedrons.png) |
Subset of a 3D-lattice (rhombohedrons) |
Two causal sets with identical past and future (for relative Cauchy evolution)
![Lightcones of a causal 3D-lattice (slab) embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice (slab).png) |
Causal set (subset of a 3D-lattice) |
![Lightcones of a causal 3D-lattice (slab, perturbed) embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice (slab, perturbed).png) |
Perturbed causal set |
![Lightcones of a causal 3D-lattice (slab, past inf.) embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice (slab, past inf.).png) |
Past subset of both causal sets |
![Lightcones of a causal 3D-lattice (slab, future inf.) embedded in 3-dimensional Minkowski spacetime](https://raw.githubusercontent.com/c-minz/Python-causets-examples/main/thumbnails/Minkowski 3D-lattice (slab, future inf.).png) |
Future subet of both causal sets |
The files operators_causal.py
and pastinf_sizes.py
are scripts that produce small data sets for plots and a data table given in my PhD thesis [1] and the publication [2].
[1] C. Minz, Algebraic Field Theory on Causal Sets: Local Structures and Quantization Methods, PhD thesis, University of York (2021).
[2] C. J. Fewster, E. Hawkins, C. Minz, and K. Rejzner, Local structure of sprinkled causal sets, Phys. Rev. D 103, 086020 (2021). https://doi.org/10.1103/PhysRevD.103.086020
The source code is published under the BSD 3-Clause License, see license file.
Copyright (c) 2020-2021, Christoph Minz