论文标题
Quaternionic量子理论仅适用于两级系统的通用动力学
Quaternionic quantum theory admits universal dynamics only for two-level systems
论文作者
论文摘要
我们重新审视量子力学在四季度上的制定，并研究该框架内的动力结构。与标准的复杂量子力学类似，然后由单一操作员介导时间演变，该操作员可以将其写入时间移动器的指数。通过对可观察到的能量和时间变化的能量之间的对应关系施加物理假设，我们证明了Quaternionic量子理论仅适用于最多两个Quaternionic dimension的系统的时间演变。将相同的策略应用于标准复杂量子理论，我们重现了Schrödinger方程决定的对应关系是唯一的选择，直到全球阶段的变化。
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.
