DSD

lie is a python mod­ule for com­pu­ta­tions with Lie groups, Lie alge­bras, rep­re­sen­ta­tions, root sys­tems, and more.

I based it on the com­puter alge­bra pack­age LiE, writ­ten by M. A. A. van Leeuwen, A. M. Cohen and B. Lisser in the early 90’s. They chose to imple­ment a pro­pri­etary script­ing lan­guage as a wrap­per for all the fancy math­e­mat­i­cal algo­rithms. While this lan­guage is use­ful for inter­ac­tive com­pu­ta­tions and short scripts, python is more expres­sive and pow­er­ful — def­i­nitely what you want when explor­ing your favorite excep­tional group.

A Fun Example

Here’s an exam­ple of using lie to do a cal­cu­la­tion that’s near and dear to every high energy theorist’s heart. We’ll show how the 10 + 5bar + 1 rep­re­sen­ta­tion of SU(5) con­tains a sin­gle stan­dard model gen­er­a­tion. First we’ll fire up python and import the lie mod­ule. Con­tinue reading…