Illustrated Glossary of Organic Chemistry

Sigmatropic reaction: A pericyclic reaction in which one or more sigma bonds are converted to an equal number of new sigma bonds via a cyclic transition state and an intramolecular process.

This [1,5]-H shift in a 1,3-diene is a sigmatropic reaction.

This Cope rearrangement of a 1,5-diene is a sigmatropic reaction, involving a [3,3]-sigmatropic shift.

This Diels-Alder [4+2] cycloaddition reaction is a pericyclic reaction, but it is not a sigmatropic reaction because it is not intramolecular, and because the number of sigma bonds lost from the reactants (one) is not the same as the number of sigma bonds gained in the product (two).