# Mobius strip and spinors

1. Aug 28, 2011

### jfy4

Hi,

I was pondering a bit about the mobius strips and I was wondering if there is a relationship between spinors and there transformation under rotations and that, in a manner of speaking, one must go around a mobius strip twice to return to the original position. To me it seems there would be some underlying relationship here.

I was thinking, abstractly, some sort of closed path, $\gamma$, with non-zero torsion; such that after traversing the loop once, one has been spun around half way, and then after a subsequent traversal, another half to return to the original orientation.

Are there such closed paths such that, say, after one traversal the torsion of the path returns one to their original orientation (a full rotation) and other paths like the one mentioned above.