Quaternionic quantum theory admits universal dynamics only for twolevel systems
Abstract
We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary which can be written as the exponential of the generator of time shifts. By imposing physical assumptions on the correspondence between the energy observable and the generator of time shifts, we prove that quaternionic quantum theory admits a time evolution for systems with a quaternionic dimension of at most two. Applying the same strategy to standard complex quantum theory, we reproduce that the correspondence dictated by the Schrödinger equation is the only possible choice, up to a shift of the global phase.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.05482
 Bibcode:
 2020arXiv200105482S
 Keywords:

 Quantum Physics
 EPrint:
 9 pages