You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more
Suppose you're a little creature living on a Möbius strip.
Then after "walking in a circle" (i.e. 2π radians), you will actually be upside-down.
In order to get back to where you started, you have to go around twice!
Check out my neat gif! 
pic.twitter.com/1MMvp83IWG
The 𝐏𝐚𝐮𝐥𝐢 𝐈𝐝𝐞𝐧𝐭𝐢𝐭𝐲 tells us how to rotate a 2 component 𝒗𝒆𝒄𝒕𝒐𝒓 of complex numbers, called a "spinor", around an axis θ̂.
for spinors, a rotation by 2π yields -1
only a rotation by 4π yields identity
..sound familiar?pic.twitter.com/ECGtLshlH2
An object that existed in a Möbius-strip-shaped universe would be indistinguishable from its own mirror image
This crab's larger claw switches between left to right with every circulation
(GIF not mine)pic.twitter.com/n3JHJdy0jJ
Fun fact: Spinor calculus already contains tensor calculus. Every tensor has a spinor analogue. A spin-vector multiplied by its complex conjugate produces a null vector.
by null vector you mean SU(N) invariant? Then i agree. What's more is that you can construct all tensor reps of SU(N) by suitable direct products of the fundamental representation!
I don’t get what this formula is saying... it’s not returning the complex vector that you get from rotating, it’s giving some scalar whose relation to the rotation is not at all clear. Can you elaborate?
It's a 2x2 matrix that acts on a 2 component complex vector (i.e. a spinor).
Besides the Euler identity, it seems to me quite related to the rotation using quaternions.
it's exactly that!
Quaternions are in fact equivalent (i.e. can de represented by) to Pauli matrices that transform (complex) vector components into 2-component spinor components via: In that sense quaternions can be spinors.pic.twitter.com/iw2rqF8rrg
I think i saw something similar in hilbert space while studying quantum mechanics. Somehow to get back where i am i rad to rotate by 4π rad ( assuming i started at |+z> and wanted to get back to |+z>) rotating by 2π rad got me to |-z>. I was creeped out
This is what happens on the Bloch's sphere where the "north" and "south" poles correspond to orthogonal states.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.
