Well, I think that I'll go on with my current approach. My draft is already deeply rooted in the tensor module, so it would take too long to rewrite it using GA, besides, I should learn the GA approach first.
Maybe GA could be used in simplification algorithms for gamma matrices with numeric indices, where its application is easy. Thanks for the idea. On Saturday, September 7, 2013 5:02:55 PM UTC+2, brombo wrote: > > On 09/07/2013 09:21 AM, F. B. wrote: > > On Saturday, September 7, 2013 1:54:35 PM UTC+2, brombo wrote: > >> 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. >> > > Well, I had a glance at the geometric algebra module, but, frankly, it > doesn't seem to be fit for my purposes. The tensor module employs abstract > tensor indices, which means we don't know their values. The geometric > algebra module instead fixes a basis. > > In the Space Time Geometric Algebra, the GA module would define (correct > me if I missed some points) the four base gamma matrices (say, *g0, g1, > g2, g3*), and the perform contractions of these expressions. This is > somehow an abstract way to handle matrix multiplication, just without the > problem to have to recognize to which expression the resulting matrix > belongs. > > The gamma matrix module should (this is my plan) handle gamma matrices > both abstractly and non-abstractly. When it comes to abstract tensors, how > can you use the GA module? I mean, the expression *G(a1)*G(a2)* is to be > interpreted as *g0*g1*, or *g2*g3*, or whatever else? We don't know which > numerical values *a1* and *a2* represent, so we have no clues on which > matrix to employ. The expression *G(a1)*G(a2)*G(a3)*G(a4)*G(a5)* is > certainly simplifiable once we know the numeric values of its indices, > because it exceeds the geometric algebra rank, but it is not if indices are > abstract. > > There are algorithms to handle gamma matrices in an abstract fashion, > and I'm going to have them in PRs. If I did not miss anything, the GA > module is not able to handle such expressions (or is it?). > > Maybe I misunderstood the GA module, in that case feel free to correct > me. > > On Saturday, September 7, 2013 2:03:17 PM UTC+2, mario wrote: >> >> I hope you go on with your program, with the simplification of products >> of gamma matrices in dimensional regularization and other standard >> tensorial tools >> for perturbative quantum field theory. >> > > I am analyzing your previous PR right now, introducing *dgamma_matr.py.* > I'll > see how to rewrite it with the new *TIDS* object, which should be faster, > and the *kahane_simplify* function already merged into master. In any > case, thanks for the tests! > > Regarding the dimensional regularization, I have already examined the > Kennedy-Cvitanovic algorithm, but before coding it, I think it's better to > have a working gamma matrix API in 4 dimensions. > > Other work to do, is to rewrite my previous ValuedTensor PR to comply > with *TIDS*, and have it included. Maybe creating a *VTIDS* object to > handle a *TIDS* with an attached *numpy ndarray*? > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] <javascript:>. > To post to this group, send email to [email protected] <javascript:>. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > > See attached example and tell me if this is what you are referring to. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
