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jdekozak / dirac5d

The Dirac equation with 5 dimensions.
GNU General Public License v3.0
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Five dimensional Dirac equation over the reals

Theoretical background

Long story made short

Starting point is an article from P Rowlands available on arxiv : http://arxiv.org/abs/quant-ph/0301071

Some articles from José B. Almeida are on Arxiv and give more hints. https://arxiv.org/search/?searchtype=author&query=Almeida%2C+J+B

And articles from Basil Hiley give the link to clifford density element to combine left and right operators. http://www.bbk.ac.uk/tpru/BasilHiley/Bohm-Vienna.pdf

Details and goals

  1. Is it possible to write the Dirac equation with geometric algebra ?
  2. Is it possible to write the Dirac equation with a geometric algebra over the reals and NOT the complex ?
  3. Is it possible to find solutions of the Dirac equation without the classical physical assumptions (eg. mass is a positive real) ?

Then,

  1. Are results from the classic Dirac equation still valid ?
  2. Are there any new results with this approach ?

    Technical stack

    • The CAS library is sympy,
    • the geometric algebra library is galgebra,
    • language is python2.

      Run with binder

      This is the easiest method, there is nothing to install, the notebook will run remotely, display is in the browser Link to binder is Binder

      Run with Jupyter notebook webserver on AWS EC2

      Computations are run on the server, only rendering is happening on the local machine. An AWS EC2 instance is properly setup with Docker and Git, ssh connection on the instance is open.

      git clone https://github.com/jdekozak/dirac5d.git
cd dirac5d
docker build --rm -t jupyter/galgebra-notebook .
docker run -p 80:8888 -e NB_UID=500 -e NB_GID=500 --user root -v /home/ec2-user/dirac5d:/home/jovyan/work jupyter/galgebra-notebook

      Run with Jupyter notebook webserver on Mac OS X

      Computations and rendering are run the local machine.

Docker must be installed https://docs.docker.com/docker-for-mac/install/

Git must be installed https://git-scm.com/download/mac

git clone https://github.com/jdekozak/dirac5d.git
cd dirac5d
docker build --rm -t jupyter/galgebra-notebook .
docker run -p 80:8888 -e NB_UID=500 -e NB_GID=500 --user root -v /home/<user>/dirac5d:/home/jovyan/work jupyter/galgebra-notebook

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