Quaternionic quantum theory admits universal dynamics only for two-level systems
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Published:2020-08-18
Issue:37
Volume:53
Page:375304
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ISSN:1751-8113
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Container-title:Journal of Physics A: Mathematical and Theoretical
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language:
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Short-container-title:J. Phys. A: Math. Theor.
Author:
Steinberg JonathanORCID,
Nguyen H ChauORCID,
Kleinmann MatthiasORCID
Abstract
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 Schrödinger equation is the only possible choice, up to a shift of the global phase.
Funder
FP7 Ideas: European Research Council
Foundational Questions Institute
Deutsche Forschungsgemeinschaft
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
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