QUATERNION QUANTUM MECHANICS

Lawrence Paul Horwitz, Lawrence C. Biedenharn

František Jenč

W. S. Anglin, Jim Lambek

Gérard G. Emch

S>The implications of group theory for the foundations of quaternionic quantum mechanics are discussed. It is proved that even in this case a relativistic description is possible. It is shown that the elementary systems for the Poincare group, as they appear in this realization, are in one-to-one correspondence with those of the usual complex quantum mechanics. The occurrence of charge conjugation related to space reflexion is discussed and some consequences on a TCP-relativistic theory are explored. The framework of a general relativistic quaternionic quantum mechanics is developed and the particular ties that exist between this theory and its complex analog are emphasized. The possible adequacy of a mixed complex-quaternionic description for isospin is discussed. (auth)

Douglas Sweetser

David Finkelstein, J. M. Jauch, David Speiser

The kinds of operators that arise naturally in quarternion quantum mechanics are indicated, and another representation theorem is given. It is shown that the logic gives rise to Hermitian operators and the dynamics gives rise to anti-Hermitian. In ordinary quantum mechanics the two are related to each other by multiplication by ih. (auth)