I don't think abstract tensors (index quantities) are a good fit with
differential geometry. A better approach is multlinear algebra as
developed in "Multilinear Algebra" by Werener Greub in which tensor
algebra, exterior algebra, and Clifford algebra are all developed on an
equal footing. In terms of Clifford algebra a spinor is the sum of a
scalar and a bivector (equivalent to antisymmetric rank-2 tensor), a
concept which is not in differential forms.
On 02/02/2014 10:23 AM, F. B. wrote:
On Sunday, February 2, 2014 1:58:52 PM UTC+1, brombo wrote:
Currently I am rewriting the geometric algebra (Clifford algebra)
and calculus module for sympy again. Current work is being kept
separately at github.com/brombo/GA <http://github.com/brombo/GA>
for now. You may want to look at tensor sections in the "GA
Notes" and "LaTeX docs" directories.
I had a glimpse at it, but that does not solve my problem (did I miss
something?).
My idea is to extend the tensor product to vectors and one-forms of
different manifolds, so a tensor like the gamma matrices can have a
differential geometric interpretation. I'm just not sure that this
approach is correct.
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