This week I have been studying and working on several things. Firstly I have been reading a long paper on ‘Holomorphic Factorization for a Quantum Tetrahedron’ which I’ll review in my next post. This is quite a sophisticated paper with some quite high level mathematics so I’ve taken my time with it.
Then I been upgrading my work on the 3d toy model including the presentation of the equilateral tetrahedron and hyperplanes as seen in the posts:
- Numerical work with Vpython and sagemath12: The Quantum Tetrahedron
- Physical boundary state for the quantum tetrahedron
- Towards the graviton from spinfoams: the 3d toy model
- Background independence in a nutshell: the dynamics of a tetrahedron
- Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
The other thing I have been working on is 1 +1 dimensional causal dynamical triangulations, starting with two main references quantum gravity ( in addition to Loll, Amborn papers) on a laptop: 1+1 cdt by Normal S Israel and John F Linder and Two Dimensional Causal Dynamical Triangulation by Normal S Israel. So far I have set up a rough framework including initial conditions, detailed balance for monte carlo analysis and initial graphical work.
What I want to be able to do is independently construct a working CDT code and build it up from 2d to 3d and finally 4d. For the 1+1 CDT code I would be aiming to be able to independently construct simulated universes which exhibit quantum fluctuations as shown below:
So far I am able to set up the initial homogeneous universe, next I will be coding the 2d Pachner move (1-2) and its inverse (2-1).
Related articles
- The SageMath Cloud – computational mathematics in the cloud (jugad2.blogspot.com)
- Grant for the search for quantum space-time (nanowerk.com)
- Dark Energy from Discrete Spacetime (plosone.org)
- Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model by Bonzom, Livine,Smerlak and Speziale (quantumtetrahedron.wordpress.com)
- Numerical work with sagemath 11: Tetrahedron Dynamics (quantumtetrahedron.wordpress.com)
- Numerical work with Vpython and sagemath12: The Quantum Tetrahedron (quantumtetrahedron.wordpress.com)
- Physical boundary state for the quantum tetrahedron by Livine and Speziale (quantumtetrahedron.wordpress.com)
