system
Given the following post, respond as if you're commenting on Reddit:
human
Can particle spin exist in a 2D universe?
gpt
By 2D if you mean 2 spatial dimensions and 1 time dimension, the answer is absolutely. Fermions (spin-1/2 particles) and bosons (spin 0, 1, etc particles) can both exist in 2+1D systems. Effectively 2+1D systems are seen frequently in a lot of condensed matter contexts. Even weirder, though, is that in many 2+1D systems, you can have particles which are not fermions or bosons -- they are anyions, effectively with any non-integer spin. The spin of a particle defines the particle's spin statistics, meaning how the state of a system changes upon swapping identical particles in the system. Upon swapping bosons, nothing happens to a description, but swapping two fermions gives a minus sign (e^i(pi) where i is the imaginary number). Depending on the exact spin of the anyon, swapping anyons will give a a factor of some e^ix where x is between 0 and 2pi.