As far as we can tell from current experiments an electron is an elementary particle that can not be divided into smaller pieces. However, in certain condensed matter systems consisting of a huge amount of electrons, there are excitations that behave as ordinary particles, and have quantum numbers that are `smaller´ than the quantum numbers of the constituent electrons. In this lecture, I will discuss this concept of `quantum number fractionalization´ using a simple toy model inspired by polyacetylene, which has fractionally charged excitations.
