Non-Tensors in GR


by thehangedman
Tags: nontensors
thehangedman
thehangedman is offline
#1
Dec13-11, 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 non-tensor 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.
Phys.Org News Partner Science news on Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior
atyy
atyy is offline
#2
Dec13-11, 11:53 PM
Sci Advisor
P: 8,005
The Levi-Civita connection can be extended to spinors (Winitzki, section 7.3.2).
haushofer
haushofer is offline
#3
Dec14-11, 09:16 AM
Sci Advisor
P: 869
The spin connection handles with fields living in "non-tensorial" representations of the Lorentz algebra in the tangent space. See e.g. Carroll's excellent notes on GR, chapter 3 :)


Register to reply

Related Discussions
Tensors Advanced Physics Homework 0
wants to learn tensors General Physics 2
More Tensors Advanced Physics Homework 15
difference between the outer product Linear & Abstract Algebra 3
relationship between tensors Differential Geometry 1