Fractionalization Quotes

The possibility and significance of fractional angular momentum is discussed, and some simple physical realizations of it are mentioned. This leads naturally to consideration of the possibility of fractional quantum statistics, which is seen to be a possibility inherent in the kinematics of 2+1 dimensional quantum mechanics. Both sorts of fractionalization are intimately related to theories, and the classic considerations of Aharonov and Bohm on the significance of the vector potential in quantum mechanics. The meaning and importance of discrete gauge invariance in continuum theories is pointed out. Fractional statistics is shown to have a simple dynamical realization in the dynamics of charge-flux tube composites. Fractional statistics is shown to occur very naturally in the most geometrical quantum field theories in 2+1 dimensions, that is in the nonlinear sigma model and in quantum electrodynamics. (Frank Wilczek)