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QMGsurvey is a Mathematica based program that can be used to analyse quantum matrix geometries, based on the algorithms from arXiv:2301.10206 (from now on [1]).
This Wiki assumes familiarity with the theory and constructions from [1]. This especially includes the sections 2.2, 2.4 and 3. For further reference, see for example arXiv:2009.03400 by Harold Steinacker on which the constructions from [1] are based.
"Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry." [1]. This package allows to analyze and visualize arbitrary matrix configurations, while a main aspect is the numerical implementation of a quantization map.
In order to use QMGsurvey, Mathematica has to be installed. QMGsurvey has been developed using Mathematica 13.1. Download the files QMGsurvey.wl and QMGxX.wl and create a new Mathematica notebook. Import both packages via
<< "\path\to\file\\QMGsurvey.wl"
<< "\path\to\file\\QMGxX.wl"where "\path\to\file" is the directory conaining the files. Alternatively, by downloading the whole package, you can directly execute the examples in the folder "examples".
QMGsurvey has been developed using Mathematica 13.1.
The following data types are frequently used:
| Type | Description |
|---|---|
| Bool | a boolean (True or False) |
| Int | an integer number |
| Real | a real number |
| Complex | a complex number |
| Real(m1,...,mn) | a real array with dimensions {m1,...,mn} |
| Complex(m1,...,mn) | a complex array with dimensions {m1,...,mn} |
| MatConf(Dim,Nim) | a matrix configuration: X in MatConf(Dim,Nim) equivalent to X in Complex(Dim,Nim,Nim) with X(a,b,c)==Conjugate[X(a,c,b)] for all indices a,b,c |
| Fx | a function |
The following standard variables occur throughout the package and are therefore collectively described here:
| Variable | Type | Description |
|---|---|---|
| Dim | Real | the (real) dimension of target space |
| Nim | Real | the (complex) dimension of the Hilbert space |
| l | Real | the (even) effective dimension of the quantum manifold |
| x | Real(Dim) | the chosen point in target space |
| X | MatConf(Dim,Nim) | the chosen matrix configuration |
Optional arguments are indicated as in var=1.23 where 1.23 is the default value of var.
The Mathematica package QMGsurvey.wl contains functions presented in:
This package contains the most important functions that build the core of QMGsurvey. The Mathematica package QMGxX.wl contains functions presented in:
The functions in this package allow for the construction of certain matrix configurations and points in target space. The general scheme of compiled functions is explained in: