Notes on Quaternion Quantum Mechanics Part I

David Speiser, David Finkelstein, J. M. Jauch

František Jenč

W. S. Anglin, Jim Lambek

Douglas Sweetser

Jerzy Dajka, M. Szopa

A. J. Davies

The quaternionic generalization of the Dirac equation is investigated. From elementary considerations of unitarity and Lorentz invariance it is demonstrated that potentials with quaternionic parts are not consistent with representation independence. This result leads to the conclusion that either quaternionic quantum mechanics singles out a special class of Dirac representations, or that allowed potentials appearing in the problem have no j or k components. If the latter alternative is the case, consideration of nonrelativistic wave mechanics casts doubt on the existence of simple experimental tests of quaternionic quantum mechanics.