On 09/07/2013 07:20 AM, F. B. wrote:
Look at geometric algebra module. if metric='[1,-1,-1,-1]' then the
basis vectors obey the gamma matrix commutation relations and all
expressions are in terms of the basis blades for the Minkowski space.
See attached.
I do not know very much of the geometric algebra module, is it
already able to handle simplification rules for gamma matrices with
GA? I already heard of the GA algebra approach to the space time
algebra, but some time ago I was told that the GA module is being
rewritten, so I skipped it.
By the way, the tensor module offers the possibility to implement an
approach much closer to standard textbooks, I am currently drafting a
/GammaMatrix/ object, we already have a highly-optimized algorithm to
reduce expressions of gamma matrices with internal Lorentz contractions.
Do you think it is worth to stop to examine the GA module instead of
going on?
Just consider that I have a clear plan in mind to go on without GA. If
we were to include GA, I should stop an devise another way.
Let me know...
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Since you are dealing specifically with the space time algebra with an
orthogonal basis you probably want something optimized to that situation
rather than a generalized Clifford algebra. I would suggest that you
look at the documentation for the GA module since that goes into detail
on how things are implemented and perhaps you might want to borrow some
code as well.
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