If |ψ> is the state of a system of two indistinguishable particles, then we have an exchange operator P which switches the states of the two particles. Since the two particles are indistinguishable, the physical state cannot change under the action of the exchange operator, so we must have P|ψ>=λ|ψ> where |λ|=1. Obviously switching the states of the two particles, and then switching them back, leaves the particles with their original states, so (P^2)|ψ>=(λ^2)|ψ>=|ψ>, so λ=±1, and thus the state of the system must be either symmetric or anti-symmetric with respect to exchange. Now I've heard that this reasoning does not hold for two dimensions, leading to the possibility of "anyons", for which you can have λ be something other than 1 or -1. How in the world is that possible? Where is the flaw or oversight in the above reasoning, that makes it exclude the 2D case? Any help would be greatly appreciated. Thank You in Advance.