OK, I found out this wikipedia article: https://en.wikipedia.org/wiki/Spinor_bundle
Apparently besides the tangent and cotangent bundles, there is also need for the spinor bundle to represent gamma matrices in the diffgeom module. On Sunday, February 2, 2014 9:11:38 PM UTC+1, Matthew wrote: > > Pinging @krastanov > > > On Sun, Feb 2, 2014 at 9:07 AM, Alan Bromborsky > <[email protected]<javascript:> > > wrote: > >> 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 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. >> -- >> 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. >> >> >> -- >> 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. >> > > -- 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.
