Inside the Knotty World of ‘Anyon’ Particles
So, I&#x27;ve been curious: having a &quot;worldline&quot; seems to imply that the objects in question are a point object -- adding one dimension (time) to zero gives you one, a line. Is this actually a reasonable model, though?<p>If we think of particles as little spheres (or loops), it should be possible to knot them -- you can knot objects 2 dimensions less than your space. (Hence, there are 1-knots in 3D and 2-knots in 4D, where an N-knot is a N-sphere embedded.)<p>Is the question of 3+1D &quot;anyons&quot; actually settled, or has no one performed the analysis on the wave equation(s) looking for 2-knots? (My reading of MS papers implied the second, but I&#x27;m hardly an expert.)<p>Ed: As an aside, Im super happy Wilzcek is covering this. I&#x27;ve always found his writing to be rather accessible.