We discuss the profound influence which the Wigner distribution function has had in many areas of physics during its fifty years of existence.

“... it ain't likely to have a radius of exactly zero,” is the conclusion of H. G. Dehmelt(1) from his Nobel Prize (1989) winning observations on trapped electrons. There are small discrepancies between Dehmelt's observations and the theoretical predictions of quantum electrodynamics (QED), which assumes that the electron is a point particle. Here we present evidence in support of Dehmelt's contention that the electron has a structure. Essentially, we point out that the nonrelativistic limit of QED is at variance with (...) a fundamental principle underlying all of physics, viz. the second law of thermodynamics. (shrink)

The phase space formulation of quantum mechanics is based on the use of quasidistribution functions. This technique was pioneered by Wigner, whose distribution function is perhaps the most commonly used of the large variety that we find discussed in the literature. Here we address the question of how one can obtain distribution functions and hence do quantum mechanics without the use of wave functions.