STATES OF ANYON MATTER

Abstract

The basic definition and elementary properties of anyons are briefly reviewed. Average field theory is introduced as a method to roughly assess the qualitative properties of aggregates of anyons, and is argued to be reliable in certain limits. The basic mechanism of anyon superconductivity is discussed in simple physical terms. The mechanism is argued to be fundamentally different from spontaneous symmetry breaking, and specifically from BCS pairing. The formal principle involved, previously discussed under the rubric "spontaneous fact violation", is given a new more precise mathematical formulation: it is the spontaneous projectivization of a linear symmetry. Tight conceptual connections are made between the fractional quantized Hall effect and anyon superconductivity, basically by inverting the average field procedure. Values of the quantum statistical parameter are identified at which anyon superconducting states are likely to occur. Values of the filling fractions are identified, as a function of the quantum statistics parameter, at which anyon quantized Hall states are likely to occur. The existence of a new state of matter, the anyon metal, is suggested, and some of its properties are roughly assessed. Possible generalizations of the ideas to cases involving inhomogeneous, three-dimensional or finite systems are discussed in a preliminary but reasonably definite fashion.