Electron Fractionalization

A largely qualitative, and rather idiosyncratic discussion of electron fractionalization in condensed matter physics is presented, including some historical reflections and some speculations concerning future application of these ideas. Particular attention is paid to systems which exhibit spin-charge separation, i.e. the electron can decay into separate excitations which carry the electron spin and the electron charge; the soliton model of polyacetylene is treated as a paradigmatic example. This paper is based on a talk given at a symposium honoring A.J.Heeger, A.G.MacDiarmid, and H.Shirakawa, the winners of the year 2000 Nobel Prize in Chemistry.