Theory of involutional transformations applied to the Dirac theory of the electron. I. Remarks on the Dirac plane waves

The involutional transformations are shown to play a fundamental role in the Dirac relativistic theory of electron. The symmetric plane waves in the momentum representation, which are the simultaneous eigenfunctions of the energy and helicity operator, are given by the columns of a unitary matrix defined by U=Y/sub E/Y/sub s/, where Y/sub E/ and Y/sub s/ are IUH (involutional, unitary, and Hermitian) matrices which diagonalize the Dirac Hamiltonian and the helicity of a free particle respectively. It is shown that all the known properties of the Dirac plane waves stem from the properties of the involutional transformations Y/sub E/ and Y/sub s/