Super Algebra Package for Mathematica

[ajb]

I have written a package for Mathematica that alters the noncommutative multiply to take into account Grassmann parity. I have also written some basic functions that may be of use.

 

It can expand expressions over the noncommutative multiply, collect terms involving Grasmann odd elements, it can give you the even and odd parts of a superfunction, it can give you the body and soul of a superfunction. I have also defined differentiation of odd variables from the left.

 

At some point I would like to extend the package to include supermatrices and calculate the supertrace and Berezinian.

 

Is there anyone on here that would like to test the package for me?

[ajb]

I have also been able to make it compatable with the add-on "VariationalMethods" by adding a few more lines of code.

 

By doing so, I have been able to get the equations of motion for (N=2) one dimensional supersymmetric quantum mechanics. I am sure more complex systems could be studied, of personal interest are BRST symmetries in (pseudo)clasical mechanics.

[ajb]

I have now put a version of this package on my website. I have also included a notebook with some elementary examples and a short article about the package.

 

It should be considered work in progress as I will continue to improve it.

 

If anyone is interested that is...

[ajb]

Just put the latest version on my website. Some bugs are fixed and some new functions added.

 

However....

 

I have also been able to make it compatible with the add-on "VariationalMethods" by adding a few more lines of code.

 

does not work any more. You get the wrong grading. I may look into this in the future.

[Severian]

I have been completely unable to get mathematica to work on my laptop

[ajb]

I have been completely unable to get mathematica to work on my laptop

 

That is a shame as I would have been very happy to see if it is of any use to anyone! I have not used it for anything "useful" yet.

 

I have written it with physics in mind, it will do some basic but useful manipulations on superfunctions like take derivatives, return the body and soul, return the even and odd parts, set the variables to zero, take the Berezin integral, expand and simplify products of superfunctions etc...

 

It could also be useful for dealing with differential forms and multivectors. I am thinking about witting another package that uses my Superalgbera packages to deal with differential forms.

[ajb]

Not that anyone is interested, but I have now added a palette that has all the commands for the package.

 

Also, I have written a further add-on for the package that defines complex conjugation using de Witt's convention. As the definition of complex conjugation relies on conventions I decided not to include it directly in my original package.