
#1
Dec1311, 10:35 PM

P: 69

I know that GR deals exclusively with tensors (at least, in every book I have), but how does the same concepts of affine connection etc extend to nontensor entities? Example would be a spinor, or even a mix of spinor / tensor. Are there different affine connections? Something different yet related (somehow) to Christoffel Symbols?
This is probably more of a pure mathematics question, but not all things in physics are tensors, and I was wondering how GR's ideas extend to these other mathematical entities. 



#2
Dec1311, 11:53 PM

Sci Advisor
P: 8,005

The LeviCivita connection can be extended to spinors (Winitzki, section 7.3.2).




#3
Dec1411, 09:16 AM

Sci Advisor
P: 869

The spin connection handles with fields living in "nontensorial" representations of the Lorentz algebra in the tangent space. See e.g. Carroll's excellent notes on GR, chapter 3 :)



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