Is there a meaning to spin of particles if it was a (1+2)D rather than (1+3)D ?
I seem to remember a link somewhere around here about spin in 2+1 Dimensions. I cannot find it though.
You could always start with:
Quantum Mechanics of Fractional-Spin Particles
Phys. Rev. Lett. 49, 957 - 959 (1982)
General Theory for Quantum Statistics in Two Dimensions
Phys. Rev. Lett. 52, 2103 - 2106 (1984)
Linking Numbers, Spin, and Statistics of Solitons
Wilczek and Lee
Phys. Rev. Lett. 51, 2250 - 2252 (1983)
There is still such a thing as spin (intrinsic angular momentum out of the plane) that describes what happens to identical particles under the exchange operation. But now things are a little different, since you no longer have spins that are quantized in units of hbar/2, but can be any real number ("anyons"). One can see this mathematically since the "Little Group" is SO(2) == U(1), which is just a phase parametrized by a real number rather than the SO(3) representations that are always 1/2-integer.
This post might be more appropriate in the QM forum, for any moderator whose watching...
The concept of spin in 2D is amazing and incredibly rich. It leads to really fancy, new physics, some of which can even possibly be realized in condensed matter systems. It's also relatively new (research on this subject got 'hot' during the '80s) and it is linked to a lot of different subjects (Braid group, topological quantum field theory, conformal field theory, fractional quantum hall effect, quantum groups, discrete gauge theories, topological quantum computers, abelian and non-abelian anyons... just to name a few ;))
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