So they touch on 4-dimensional theories only briefly, but one thing I'm very curious about is if higher dimensional theories provide a richer computational structure, in any of several senses.<p>Every 1-knot has a sort of 2-knot analog (actually, a whole family of them) made by "revolving" the knot, but there are 2-knots not generated in this manner. (The same holds true for higher dimensional knots.)<p>As we go higher, there are knot moves not even possible in lower dimensions (such as twists).<p>Just a thought.
"Elementary particles are elementary excitations of the vacuum, which explains why they are identical." (pg 4 ref 3) Is this now accepted fact, everything is a wave and there are no particles?
Has someone found a particle for which some exchange yields something like a magic state? I've been told that known nonabelian anyons can only be exchanged up to Cliffords