Quaternionic quantum theory admits universal dynamics only for two-level
systems
- URL: http://arxiv.org/abs/2001.05482v2
- Date: Wed, 22 Jul 2020 18:45:57 GMT
- Title: Quaternionic quantum theory admits universal dynamics only for two-level
systems
- Authors: Jonathan Steinberg and H. Chau Nguyen and Matthias Kleinmann
- Abstract summary: We prove that quaternionic quantum theory admits a time evolution only 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 Schr"odinger equation is the only possible choice.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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
operator 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 only 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
Schr\"odinger equation is the only possible choice, up to a shift of the global
phase.
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