17 and 24 Sep 2020
Jerzy Kocik
Taking square roots in higher dimensions
-- spins, polarization, and a little metaphysics
[Recording of part 1] [Recording Part 2]
Borzu shared the link with this cool video on related toy
and this 3D-printable file . Check it out!
See also Copernicus Theorem at Wolfram, at Cut-the-knot, at Mathematics.
Cf. Tusi couple.
Great talk, thanks a lot. By the way, electric field is always associated with magnetic field and complex description is also at this level, look at the book by Bateman, H. The Mathematical Analysis of Electrical and Optical Wave-Motion from early 20th century. This is very much like what was presented. In modern approach consider the electromagnetic field as a two-form $F=F_{\mu \nu}dx^{\mu}\wedge dx^{\nu}$ and then $F\wedge *F$ will, when written in terms of electric and magnetic field will have parts like $\vect{E}^2-\vect{B}^2$ and $2\vect{E}\cdot\vect{B}$, which correspond to what was discussed in polarization, Poincare sphere part of the talk. Perhaps very worthy to look at papers by Robinson and Trautman on optical geometry.
ReplyDeleteSorry, some formulas apparently did not work, try again:
ReplyDelete$\vec{E}^2-\vec{B}^2$
$2\vec{E}\cdot\vec{B}$