Numerical work with sagemath 13: 1+1 causal dynamical triangulations

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:



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.

cdt1+1 fig

cdt1+1 figb


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:

cdt1+1 fig1


2 thoughts on “Numerical work with sagemath 13: 1+1 causal dynamical triangulations”

  1. Dear David,

    interesting to read your contribution on CDT. I’m a physicist by background and ended up in Chemical Engineering (real fun). However I have a continued interest in the basics of physics and got interested in the work of Renate Loll on CDT. I would really like to set-up some toy-model for this, to get some true experience in the subject. As you do have such a model I wondered if it would be possible to have a copy of your code, so I have a working starting point.

    thanks in advance for your help,

    best regards,

    Joop Baltussen

    ps. in return you might a look to my piano pieces on youtube 🙂

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