[p,q] does not equal (i h-bar)

Abstract

In this short note, I point out that [p,q] does not equal (i h-bar), contrary to the original claims of Born and Jordan, and Dirac. Rather, [p,q] is equal to something that is *infinitesimally different* from (i h-bar). While this difference is usually harmless, it does provide the solution of the Born-Jordan "trace paradox" of [p,q]. More recently, subtleties of a very similar form have been found to be of fundamental importance in quantum field theory.