Sagemath 19 part 1: The spectrum of the Ricci operator for a monochromatic 4 – valent node dual to an equilateral tetrahedron

This week thanks to some colleagues I have  been working on the spectrum of the Ricci operator for a monochromatic 4 – valent node dual to an equilateral tetrahedron. This blog post reports on working in progress,

 

I have been reviewing the papers seen in the posts:

Basically I am porting Mathematica code over to sagemath so that I can then use it it the calculation of the matrix elements of the  LQG Hamiltonian Constraint operator discussed in the  in the posts:

So far I have written code for a number of operators, but I still have the same number still to do, After this I’ll need to join them together.

The matrix defining the operator Q {e1, e2, e3} used in the definition of the volume operator

mono1

H ithe matrix defining the operator δij.Yi.Yj used to define the length operator expressed in the intertwiner basis

mono2

And B the intertwiner basis

mono3

When complete I’ll be able to produce graphs such as those below which is a plot of the spectrum of R as a function of the spin. This can then e used in The numerical investigation of the LQG Hamiltonian Constraint Operator.

 

mono5

 

 

Enhanced by Zemanta
Advertisements

2 thoughts on “Sagemath 19 part 1: The spectrum of the Ricci operator for a monochromatic 4 – valent node dual to an equilateral tetrahedron”

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s