causal-sets quantum-gravity causal-set-theory causets

Introduction

This repository contains some example functions and scripts that use my Python modules causets.

Animations

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

de Sitter spacetime, 1-simplex

Lightcones of a causal 2-simplex embedded in 3-dimensional de Sitter spacetime

de Sitter spacetime, 2-simplex

Lightcones of a causal 1-simplex embedded in 2-dimensional Minkowski spacetime

Minkowski spacetime, 1-simplex

Lightcones of a causal 2-simplex embedded in 3-dimensional Minkowski spacetime

Minkowski spacetime, 2-simplex

Lightcones of a causal 2-simplex with one edge flipped embedded in 3-dimensional Minkowski spacetime

Minkowski spacetime, 2-simplex with one edge flipped

Lightcones of a causal 2-simplex with two edges flipped embedded in 3-dimensional Minkowski spacetime

Minkowski spacetime, 2-simplex with two edges flipped

Lightcones of a causal 3-simplex embedded in 4-dimensional Minkowski spacetime

Minkowski spacetime, 3-simplex

Lightcones of a causal 1-simplex embedded in 2-dimensional Schwarzschild spacetime

Schwarzschild spacetime, 1-simplex

Subsets of lattices in Minkowski spacetime

Lightcones of a causal 2D-lattice embedded in 2-dimensional Minkowski spacetime

Subset of a 2D-lattice

Lightcones of a causal 3D-lattice of octahedrons embedded in 3-dimensional Minkowski spacetime

Subset of a 3D-lattice (octahedrons)

Lightcones of a causal 4D-lattice of octahedrons embedded in 4-dimensional Minkowski spacetime

Subset of a 4D-lattice (octahedrons)

Lightcones of a causal 3D-lattice of octahedrons embedded in 3-dimensional Minkowski spacetime (smaller subset)

Smaller subset of a 3D-lattice (octahedrons)

Lightcones of a causal 3D-lattice in FCC embedded in 3-dimensional Minkowski spacetime

Subset of a 3D-lattice (FCC)

Lightcones of a causal 3D-lattice in HCP embedded in 3-dimensional Minkowski spacetime

Subset of a 3D-lattice (HCP)

Lightcones of a causal 3D-lattice of rhombohedrons embedded in 3-dimensional Minkowski spacetime

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

Causal set (subset of a 3D-lattice)

Lightcones of a causal 3D-lattice (slab, perturbed) embedded in 3-dimensional Minkowski spacetime

Perturbed causal set

Lightcones of a causal 3D-lattice (slab, past inf.) embedded in 3-dimensional Minkowski spacetime

Past subset of both causal sets

Lightcones of a causal 3D-lattice (slab, future inf.) embedded in 3-dimensional Minkowski spacetime

Future subet of both causal sets

Other scripts

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

License information

The source code is published under the BSD 3-Clause License, see license file.

About

Python (version 3.8) examples (with mypy typing support) for the package in c-minz/Python-causets.

causal-sets quantum-gravity causal-set-theory causets

BSD 3-Clause "New" or "Revised" License

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